James Murdoch will be criticised by MPs investigating phone hacking on Tuesday, but their assessment of his conduct is expected to fall just short of accusing the former chairman of News International of misleading parliament about the extent of his knowledge of the affair.

The all party culture media and sport select committee concluded they could not reach a final decision about whether Murdoch misled them because of what the MPs described as conflicting evidence, according to a source close to the process. However, there was enough to lead members to agree that Murdoch had not asked the questions that would help determine the true extent of phone hacking at the News of the World for several years.

Some Conservatives on the committee are understood to have argued that Murdoch should not have been criticised at all, but in a three-hour meeting, in which much of the debate was taken up with agreeing the final wording as regards the News Corporation heir, their amendments are understood to have failed.

News International now concedes in civil actions brought by hacking victims that illegal practice took place at the News of the World between 2001 and 2006, before Murdoch became executive chairman in late 2007.

However, News International admits that it did not appreciate the extent of hacking until the very end of 2010, when it saw fresh evidence in a case involving the actor Sienna Miller.

Murdoch appeared before the select committee in both July and November, and the outspoken Labour MP Tom Watson described him as acting like a mafia boss at that second hearing – a contention rejected by Murdoch. It fell to Damian Collins, a Conservative, to come closer to the committee's final conclusions, saying: "It may not be the mafia, but it doesn't sound like Management Today."

The select committee will reserve some of its strongest condemnation for Murdoch's predecessor in the role, Les Hinton, who had appeared before the committee three times over the past five years. Hinton told the committee last October that he was right to have told MPs in 2009 that phone hacking was not rife at the newspaper.

Hinton is expected to be accused of misleading parliament as a result, with MPs particularly focused on his evidence as regards Clive Goodman, the former News of the World royal editor, who went to jail for hacking in 2007.

Goodman subsequently made an unfair dismissal complaint, saying hacking was "widely discussed" until reference to it was banned by the then editor. But Hinton said the complaint was unfounded, and amounted to "accusations and allegations".

The parliamentary report will also criticise the former News of the World editor Colin Myler and the newspaper's long serving chief lawyer Tom Crone in a long awaited document due to be released on Tuesday.

Myler, who is now editor of the New York Daily News, and Crone had been repeatedly pressed on their failure to uncover what had happened.

However, Rebekah Brooks and Andy Coulson, the two previous editors of the Sunday tabloid when phone hacking took place, will not be singled out, because both have been arrested on suspicion of involvement in the intercepting of voicemail messages.

Committee members felt they could not condemn indiduals who had been arrested – providing some relief for David Cameron, who appointed Coulson as his chief spin doctor after Coulson resigned from the News of the World after Goodman was jailed.

Individuals found guilty of misleading parliament can be called to the bar of the Commons to apologise.

James Murdoch's father, Rupert, who gave evidence to the committee last July shortly after shutting the News of the World, is not accused of misleading parliament. But the MPs' report is understood to be critical of the corporate culture of News International, the UK subsdiary of his News Corporation, and the immediate parent company of the News of the World.