John Prescott's affair with one of his secretaries could be investigated if it breaks any civil service rules, a standards watchdog has said.
The affair is reported to have started at an office party
The deputy prime minister says he regrets the relationship with Tracey Temple, which ended "some time ago".
Sir Alistair Graham, head of the Committee on Standards on Public Life, said private behaviour was an issue only if it affected ministers' jobs.
In this case issues might emerge because a civil servant was involved.
Sir Alistair added that if there had been any breach of civil service rules "I'm sure the Cabinet secretary will investigate them and deal with them appropriately".
He told the Commons public administration committee the public made a distinction between public officials' private lives and their public jobs.
Conservative MP Andrew Robathan complained that Mr Prescott had long dodged his questions about guests at his official country residence of Dorneywood.
Mr Prescott reportedly took Ms Temple to the 21-room house in Buckinghamshire.
The Tory MP said he had taken her there in an official car at the public expense and claimed Mr Prescott did not think the rules applied to him.
Asked if Mr Prescott was guilty of abusing ministerial privilege, Sir Alistair said people could make allegations about breaches of the ministerial code of conduct about such issues.
Mr Prescott issued a statement on Wednesday voicing his regret over the affair.
"I have discussed this fully with my wife Pauline who is devastated," he said. "I would be grateful if [we] can get on with our lives together."
Mr Prescott gave a forced smiled to waiting camera crews and said nothing as he left a Cabinet meeting on Thursday. Tony Blair's spokesman said Mr Prescott had strong support and was a "real benefit" to the country and government.
The spokesman added that Mr Prescott, 67, played "an absolutely vital role".
Downing Street had earlier said it was a "private matter", a message repeated by Work and Pensions Secretary John Hutton when he appeared on BBC Radio 4's Today programme.
Mr Prescott and Ms Temple started meeting in secret at his Whitehall flat after a two-year relationship began at an office party in 2002, the Daily Mirror reported on Wednesday.
The pair had a two-year relationship
The pair began working together when Ms Temple was appointed as Mr Prescott's assistant private secretary, responsible for organising his diary, said the paper.
She had reportedly previously worked as a personal diary secretary for former Northern Ireland Secretary Mo Mowlam, who died of cancer last year.
The PM's spokesman said Mr Prescott had not offered to resign, nor had he abused his position by having an affair with a civil servant.
Ms Temple's boyfriend, lorry driver Barrie Williams, 46, told the Daily Mirror: "I just can't believe that my darling Tracey has been sleeping with John Prescott behind my back.
"How dare he split up my relationship with the woman I'd planned to marry!"
Mr Williams, of Bordon, Hants, said Ms Temple asked him to marry her just two days after she began a relationship with Mr Prescott.
Mr and Mrs Prescott have been married for more than 44 years and have two children.
The Daily Mirror's assertion that the affair was common knowledge in Mr Prescott's department was dismissed by Local Government Minister Phil Woolas.
"I think it is a private matter for the deputy prime minister," he said.
"I have worked for him for many years and I have every confidence in his ability, not just as a public spokesperson for the government but as the chair of Cabinet committees and as deputy to the prime minister and standing in for him, and in leading his department."