The BBC has taken legal advice on whether it can recoup some of the £450,000 payoff given to director-general George Entwistle, Lord Patten said today.
But the chairman of the BBC Trust said he doubted a bid to get some of the money back would be successful.
The corporation has been accused of a "cavalier" attitude towards licence fee money over the payoff.
Mr Entwistle resigned after just 54 days in the job as a result of his handling of the fallout from the Jimmy Savile crisis, and was paid the money - twice the amount to which he was entitled - in order to speed up his departure.
A report by the Public Accounts Committee was scathing, saying it was "out of line both with public expectations and what is considered acceptable elsewhere in the public sector".
It said further benefits paid to him were "an unacceptable use of public money".
MPs also criticised "excessive" severance payments to 10 other senior managers, including former chief operating officer Caroline Thomson who received £670,000 when she left this year.
During the committee's hearing last month, MPs accused the BBC of offering her a large redundancy sum as "compensation" when she failed in her bid to become DG.
The report is the latest blow to the BBC, after a review by former Sky News executive Nick Pollard - published yesterday - painted a picture of a top-down organisation beset with rivalries and faction fighting.
It found the decision to drop a Newsnight report into Savile's decades-long campaign of sexual abuse plunged the BBC into "chaos and confusion", revealing a corporation where "leadership and organisation seemed to be in short supply".
Lord Patten told the BBC Radio 4 Today programme: "We've taken legal advice about whether we could actually take any money back.
"In order for us to do so we have to be able to argue that, on the basis of what Pollard says, it would have been justified to make a summary dismissal of the former director-general and I rather doubt whether we will get the legal go ahead for that."
He said that with "hindsight" the Trust chose the wrong candidate for the top job, and said if the BBC had refused Mr Entwistle's payoff claim it would have ended up in "an appalling mess" in the courts.
"It was precisely because we were dealing with public money and a great public service broadcaster that we took the view that it was more sensible to settle for the amount that we were being asked for rather than fetch up paying more for a constructive dismissal," he said.
The committee report said MPs were "extremely concerned" that the BBC Trust - which agreed the payoff to Mr Entwistle - had rejected an offer for the National Audit Office to examine the package for the ex-DG, who stepped down on November 10.
"This inhibited Parliament's ability to hold the Trust to account for its use of public money," the report said.
Mr Entwistle would normally have been entitled to £225,000 - half his salary - if he had voluntarily resigned.
But the Trust agreed to the larger amount to allow a speedy clean break, allowing them to draw a line under the episode and seek a new DG without lengthy legal negotiations.
The committee concluded: "By agreeing to this payment, the BBC Trust may have secured the director-general's quick departure but it did not act in the wider public interest. Public servants should not be rewarded for failure."
Mr Entwistle's other benefits under the deal drew further criticism. On top of his salary payoff, he was given a year's private medical cover and contributions to his legal costs.
The committee said it considered the additional benefits to be "an unacceptable use of licence fee payers' money".
Margaret Hodge, who chairs the committee, warned out-of-touch BBC executives risked inflaming "dangerous" calls for the broadcaster to be subject to more political oversight.
"I don't think the BBC gets it and doesn't understand public opinion," she told BBC Radio 4's Today.
The MPs' investigation found 10 senior executives had left recently with more than £250,000 and that more than 400 senior executives got private healthcare packages, she said.
"For our money, through the licence fee, to be used to fund public servants accessing private healthcare just doesn't seem right."
She said there was "a disparity between those... who don't get paid a lot and who work because they are committed to public service broadcasting and then a management tier who I think just don't get it.
"They don't get it that they are being paid through the licence fee, which is a form of taxation, and they don't understand that people find this astonishing.
"When you find behaviour like this where the BBC appears just not to understand how the public feel about the way their money is used, what you then get is you rekindle the argument about 'have we got the right structure, should the BBC be more accountable to parliamentarians or to government?'
"I think that is dangerous."