John Whittingdale, the Conservative MP who chairs the culture committee, particularly intends to ask Murdoch to clarify statements he made about a key email which is thought to suggest that knowledge of phone hacking at the News of the World went beyond one "rogue reporter".
The move comes after two former News of the World executives contradicted Murdoch's assertion at a hearing of the culture committee in July that when a six-figure payment was signed off to phone hacking victim Gordon Taylor, it was done without all the facts being known.
Former News of the World legal manager Tom Crone and ex-editor Colin Myler have refuted that claim, telling the MPs last week that the email was "the reason that we had to settle the case".
When the email was sent, the paper's royal editor Clive Goodman had already been jailed for hacking into the phones of members of the royal household.
The News of the World insisted that the practice was down to just one "rogue reporter", but the email is thought to have implied that the paper's former chief reporter Neville Thurlbeck was also implicated in malpractices.
The date of Murdoch's proposed appearance in front of the MPs has not yet been finalised, but reports suggest that the hearing could go ahead in November.
A News Corp spokesperson said: "We await details of the committee's request, however James Murdoch is happy to appear in front of the committee again to answer any further questions members might have."
Separately, it has emerged that the mother of a London 7/7 bombing victim is to pursue a civil case against News International over claims that the News of the World hacked into the voicemails of people who lost loved ones in the terrorist attacks of 2005.
Sheila Henry, whose son Christian Small was killed in the Russell Square explosion, is to be one of six test cases against the News of the World publisher News Group Newspapers.
Lord Justice Vos has been considering applications at the High Court from a number of alleged phone hacking victims to decide whose test cases will be heard in the new year.
Other legal cases in contention include actor Jude Law, MP Chris Bryant, interior designer Kelly Hoppen, sports agent Sky Andrew and ex-footballer Paul Gascoigne.