The Home Secretary suggested further action could be taken following the publication of the Dyson report into the interview by Martin Bashir.
It comes after the report concluded the journalist used “deceitful behaviour” to land his world exclusive 1995 interview and an internal BBC investigation had covered it up.
Asked on Sky News’s Trevor Phillips on Sunday about the prospect of prosecutions, Ms Patel said: “If there is subsequent action that needs to be taken, then clearly – alongside the publication of this report and lessons being learned and changes, changes to the institution, structure, governance, accountability – then that will follow.”
She claimed the BBC’s reputation has been “compromised” by the disclosures and warned the forthcoming mid-term review of the BBC charter would be a “very, very significant moment” for the corporation.
She said: “There will be an opportunity not only for reflection but an opportunity to look at governance reforms and how effectively accountability and governance can be strengthened.
“There will be a very, very significant moment now – there is no question about this – where lessons have to be learned.
“The BBC itself – one of our great institutions – its reputation has been compromised.
“They themselves will have to reflect upon the report and spend a great deal of time really looking at how they can regain and rebuild trust and confidence.
“They will have a great deal of work to do in this particular area. Right now is a very, very important time for the BBC to very much look at itself and learn very important lessons from the publication of this report.”
Scotland Yard has said it will study the report’s findings to assess whether it contains any “significant new evidence”.
Lord Dyson said Mr Bashir was in “serious breach” of the BBC’s producer guidelines after he faked bank statements and showed them to Diana’s brother Earl Spencer to gain access to the princess.
Mr Bashir had been cleared by internal inquiry in 1996, led by former director-general Lord Tony Hall, even though he had previously admitted lying about the fake documents he used in obtaining the interview.
Speaking to the Sunday Times, the journalist insisted he “never wanted to harm” Diana with the interview.
He told the newspaper: “I never wanted to harm Diana in any way and I don’t believe we did.
“Everything we did in terms of the interview was as she wanted, from when she wanted to alert the palace, to when it was broadcast, to its contents … My family and I loved her."
Mr Bashir also apologised again for commissioning documents purporting to show payments into the bank accounts of members of the royal household.
He said: “Obviously I regret it, it was wrong.
“But it had no bearing on anything. It had no bearing on [Diana], it had no bearing on the interview.”
Current director-general Tim Davie wrote to BBC staff on Friday saying: “I know that we now have significantly stronger processes and governance in place to ensure that an event like this doesn’t happen again.
“However we must also learn lessons and keep improving.”