Conservative MP John Whittingdale, who is chair of the Culture Committee, said the former Mirror editor could be quizzed by the Metropolitan Police on the basis of recent evidence.
Labour also stepped up the pressure on Mr Morgan, who now hosts a chat show on CNN, with deputy leader Harriet Harman saying he has questions to answer over the affair.
It comes just a day after Sir Paul McCartney’s former wife Heather Mills claimed that a journalist from the Mirror Group admitted targeting her phone in 2001.
Although the journalist was not Mr Morgan, he was editor of the Daily Mirror at the time and the message Ms Mills referred to was one that he admitted hearing in a 2006 article for another newspaper.
At that time Mr Morgan wrote: “At one stage I was played a tape of a message Paul had left for Heather on her mobile phone.
“He sounded lonely, miserable and desperate, and even sang We Can Work It Out into the answer phone.”
Ms Mills told the BBC that in 2001 a journalist had rung her quoting part of the message and, when challenged, he admitted that her phone had been hacked.
Following the claims, Mr Morgan described the allegations as “unsubstantiated” and said: “I have never hacked a phone, told anyone to hack a phone, nor to my knowledge published any story obtained from the hacking of a phone.”
He also claimed that Ms Mills herself had been accused of phone hacking.
In a statement he said: “What I can say, and have knowledge of, is that Sir Paul McCartney asserted that Heather Mills illegally intercepted his telephones, and leaked confidential material to the media. This is well-documented, and was stated in their divorce case.”
But Labour said that it was “not good enough” for Mr Morgan to say he had always kept within the law.
“There are questions about what happened with Heather Mills’s phone messages that he needs to answer,” Ms Harman said.
Therese Coffey, a Tory MP and a member of the Culture, Media and Sport Select Committee investigating phone hacking, also called for Mr Morgan to return to the UK to help the police with their inquiries.
Mr Whittingdale later added: “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 added the committee did not have the power to compel people to return to the UK to face questions.
“I’m sure the committee will want to talk about it when we meet but Parliament is in recess at the moment,” said Mr Whittingdale. “The police investigation is ongoing and that 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 must not interfere 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.”
Mirror Group has said that all its journalists acted within the law.
Mr Morgan tweeted last night: “So heart-warming that everyone in UK’s missing me so much they want me to come home.”