Following a damning report from MPs into his appointment, pressure is mounting on BBC chairman Richard Sharp.
The committee found that while applying for the position, he made "significant errors of judgment" by acting as Boris Johnson's go-between on a loan.
Mr. Sharp's position is "extremely difficult," SNP committee member John Nicolson told the BBC.
Mr. Sharp asserted that he neither helped set up a guarantee for the loan nor offered Mr. Johnson any financial guidance.
Mr. Sharp's position was described as "increasingly untenable" by Labour's Lisa Nandy on BBC's Sunday With Laura Kuenssberg.
Since the Sunday Times first reported the claims last month, Mr. Sharp's role in Mr. Johnson's acquisition of a £800,000 loan guarantee has come under scrutiny.
Businessman Sam Blyth, a distant relative of Mr. Johnson and a friend of Mr. Sharp, allegedly suggested serving as a loan guarantor for Mr. Johnson in 2020.
The Commons Digital, Culture, Media and Sport (DCMS) Committee supported Mr. Sharp's appointment at the time he was named as the government's top choice for the BBC chairmanship in January 2021.
On the advice of the culture secretary, who is in turn advised by a panel, the prime minister ultimately makes the government's selection.
The committee called the BBC chairman to testify this week, and the committee's report was released on Sunday.
He claimed in his remarks to MPs that he had introduced Mr. Blyth, a friend, to the Cabinet Office.
The cross-party committee criticized Mr. Sharp for failing to mention any involvement he may have had in the loan-related events when they were evaluating his qualifications for the position two years ago in their report.
His choices to "become involved in the facilitation of a loan to the then-prime minister while at the same time applying for a job that was in that same person's gift" and failure to disclose this to the committee, according to the report, undermined confidence in the public appointment process.
"Mr. Sharp should think about the effect his omissions will have on trust in him, the BBC, and the public appointment process," the MPs said in their conclusion.
The report is carefully worded and does not state in no uncertain terms that he should resign. A diplomatic way of bringing up that point is when it says he should "consider the impact" of what has happened.
The SNP's Mr. Nicolson went further than the report on Sunday With Laura Kuenssberg, claiming that Mr. Sharp's position was "extremely difficult" because he "broke the rules".
"He has clearly lost the staff's trust at the BBC," he said.
"On the job application, you are asked if there is anything about your relationships with others that might embarrass you.
"This has undoubtedly embarrassed me.
Mr. Nicolson claimed that Mr. Sharp had not disclosed to MPs that he had helped Mr. Johnson obtain an £800,000 loan; Mr. Johnson "then gave him the job.".
It all has a banana-republic vibe, he continued.
Andrew Mitchell, a cabinet minister, stated on the same program that the BBC would make the decision regarding Mr. Sharp's future. A review of his hiring by the watchdog that monitors public appointments, he added, should be delayed.
However, during the program, he was pressed on this because, in accordance with the BBC charter, the government, not the BBC, is the only entity that has the authority to remove the chairman from his or her position.
According to Lisa Nandy, the shadow leveling up secretary, it is "right that the BBC is able to publish" its own investigation into Mr. Sharp's appointment and that "due process is followed.".
However, she continued, if issues persisted after the BBC's report was released, "the integrity of the BBC is more important than one individual.".
This week, Mr. Sharp informed the committee that he had spoken with Cabinet Secretary Simon Case in December 2020 to obtain authorization to give him businessman Mr. Blyth's contact information.
However, he revealed to Mr. Case during the same meeting that he had applied for a position with the BBC, and the two agreed that he would have "no further participation" in order to avoid any potential conflicts of interest or perceptions of conflicts as a result of his application to the BBC.
MPs on the DCMS stated in their report that Mr. Sharp had acknowledged the need for "open and transparency" by bringing it to the cabinet secretary's attention, but "failed to apply the same standards of openness and candor in his decision not to divulge this information during the interview process or to this committee during the pre-appointment hearing [for the BBC job].".
"Mr Sharp's failure to disclose his actions to the panel and the committee, although he believed this to be entirely proper, constitute a breach of the standards expected of individuals applying for such public appointments," the report continued.
According to a representative for Mr. Sharp, he did not arrange for Mr. Johnson and Mr. Blyth to meet, and he was not involved in their loan arrangement.
"Mr. Sharp acknowledges that the committee felt that certain information from his pre-appointment hearing should have been disclosed to it. He is sorry and expresses regret.
"Mr. Sharp acted in good faith in the manner he did because he was trying to follow the rules at the time and thought he had succeeded in doing so.
The spokesperson continued, "Mr. Sharp believed he had dealt with the issue by proactively informing the cabinet secretary that he was applying for the position of BBC chair, and so beyond connecting Mr. Blyth with Mr. Case, he recused himself from the matter.
The DCMS Committee report also criticized ministers who defended the choice to support Mr. Sharp in 2021 after the loan dispute broke out despite the fact that they were not informed of the circumstances.
"It is highly unsatisfactory that ministers have used this committee's original report on Mr. Sharp's appointment as a defense of the process was followed, when we were not fully in possession of all the facts that we should have had before us to reach our judgment," the report stated.
The BBC chairmanship was given to Mr. Sharp after two "transparent and rigorous" hiring processes, according to Prime Minister Rishi Sunak, who also noted that the appointment was made by his predecessor.
The Sunday Times claims that a leaked memo from Mr. Case advised Mr. Johnson to "no longer" seek financial advice from Mr. Sharp.
However, the MPs claimed in this latest report that there was still a "unresolved issue" regarding why the cabinet secretary had assumed Mr. Sharp had been providing financial advice to Mr. Johnson. They urged the Cabinet Office to "clear up the confusion relating to the advice given to the prime minister immediately" given that Mr. Sharp had claimed this was not the case.
We don't comment on leaks, a Cabinet Office spokesperson said.
Richard Sharp's appointment is still under investigation by the Office of the Commissioner for Public Appointments.
Additionally, the BBC is conducting its own internal investigation into any potential conflicts of interest that Mr. Sharp might have in his position as BBC chairman.
The completion date for any of these reviews is unknown.