Ofcom says it is considering a request to re-examine whether James Murdoch is fit to run a broadcaster.
ITV News has seen a copy of letter sent to Sharon White, Ofcom's chief executive, by a group of prominent politicians asking her to carry out a new inquiry.
Ofcom investigated James Murdoch's conduct as an executive following the phone-hacking scandal at the News of the World and The Sun.
In September 2012 the regulator judged that his behaviour as chief executive and chairman of News Group Newspapers "repeatedly fell short of the conduct expected of him" but decided that there was "no reasonable basis to conclude" he was involved in any wrong-doing.
Ofcom also took the view that Sky (then called BSkyB) was a fit and proper owner of a broadcast license.
Ed Miliband, Sir Vince Cable, Baroness Warsi, Baroness O'Neill and Lord Falconer want that decision reassessed.
In their letter they argue that since the last review "there has been an extraordinary pattern of criminality and wrong-doing revealed at News International" and "new allegations in open court" that James Murdoch authorised the deletion of emails after the scandal broke.
This is personal. Ed Miliband told me that since that last review James Murdoch's influence as a director has grown (he's now chief executive of 21st century Fox and chairman of Sky) and he argues it will extend further if Fox's takeover of Sky proceeds.
You may recall that in December last year, Fox tabled a bid to take full control of Sky - a company it currently owns a 39% stake in.
What's interesting is that Ofcom has an ongoing duty to ensure companies that hold a broadcast licence are fit and proper. It raised no objections when James Murdoch returned to Sky as chairman last year, rather suggesting it doesn't share Ed Miliband's concerns.
This is an obvious attempt to sabotage the Sky takeover by a coalition of individuals whose dislike of the influence Rupert Murdoch has on British politics is well established.
Ofcom is considering how to respond. Ed Miliband told me he would be "surprised" and "it would be a failure of the regulator if they say there's nothing to see here".
ITV News has contacted Sky and Fox for comment.