Former Daily Mirror editor Piers Morgan should return to the UK to answer "some very serious questions" over allegations of phone hacking, the Culture Committee chairman said today.
Conservative MP John Whittingdale said Mr Morgan could be quizzed by the Metropolitan Police on the basis of recent evidence.
But he said Mr Morgan would not immediately be called in front of the Commons Culture, Media and Sport Committee, which is investigating phone hacking, because the police inquiry "has to be the priority".
His remarks came after Heather Mills claimed that a senior Mirror Group journalist admitted hacking voicemails left for her by Sir Paul McCartney.
Sir Paul's former wife told BBC2's Newsnight that the journalist made the admission in 2001.
The BBC, which declined to name the journalist allegedly involved, said it was not Mr Morgan, who was editor of the Daily Mirror at the time.
But the message in question appeared to be the same as one which Mr Morgan later admitted listening to, a spokesman for the programme said.
In a 2006 article in the Daily Mail, Mr Morgan referred to hearing a recorded message which Sir Paul had left for Ms Mills, the spokesman said.
He wrote: "At one stage I was played a tape of a message Paul had left for Heather on her mobile phone."
Mr Morgan issued a statement describing Ms Mills' claims as "unsubstantiated".
Tory MP Therese Coffey, a member of the Culture Committee, called on Mr Morgan to help the police in the light of the "very strong" new evidence.
"I just hope that the police take the evidence and go with it and if Mr Morgan wants to come back to the UK and help them with their inquiries - and I don't mean being arrested in any way - I'm sure he can add more light," she told Newsnight.
"I think it would help everybody, including himself and this investigation, if he was able to say more about why he wrote what he did in 2006."
Mr Whittingdale told the BBC News channel: "What Therese Coffey has said is absolutely right - I would like to see Mr Morgan come back to this country and answer what are some very serious questions."
He said the committee did not have the power to compel people to return to the UK to face questions.
"Now he may return to the UK, I hope he will return to the UK and I imagine that there will be some questions which will be put to him, possibly by the police on the basis of the evidence that has emerged," he said.
"But at the moment, we can't do that. I'm sure the committee will want to talk about it when we meet but Parliament is in recess at the moment, the police investigation is ongoing.
"And the police investigation has to be the priority."
Mr Whittingdale said the committee's inquiry was currently restricted to looking at whether it was "previously misled in the evidence we were given in relation to the News of the World".
He added: "We mustn't interfere obviously with an ongoing police investigation and it seems that the kind of evidence that is now emerging which may implicate the Daily Mirror is something that the police need to look at and look at quite quickly."
In a statement issued through CNN last night, Mr Morgan said: "Heather Mills has made unsubstantiated claims about a conversation she may or may not have had with a senior executive from a Trinity Mirror newspaper in 2001."
He said the BBC had confirmed to him that the executive was not employed by the Daily Mirror, adding that he had no knowledge of any conversation any executive from other Trinity Mirror newspapers "may or may not have had with Heather Mills".