Major shareholders in Granada, including the Capital Group, Barclays Bank and Legal & General, are said to want Allen to step down from the company. Granada was the joint parent of ITV Digital with ITV partner Carlton Communications.
Allen has come under fire for trying to bury ITV Digital's problems by reigniting speculation about a merger between Carlton and Granada.
Last week, just days after ITV Digital was officially put up for sale and its digital licence put out for tender, Allen announced that he wanted to reignite merger talks with Carlton to create a single ITV company.
However, senior figures at Carlton have poured water on Allen's hopes by criticising him for talking to the newspapers about his intentions before speaking to them.
Carlton has also made it clear that if Granada, the bigger of the two companies, wants to take over Carlton it will have to pay a hefty premium for the firm. So far, Allen has failed to address the issue of how much Granada would offer for its smaller rival.
News of Allen's potential fall will scupper recent speculation that he, along with Carlton chairman Michael Green, would lead a merged company once broadcasting regulations ruling out a merger are removed. This is due to be set out in today's draft communication's bill.
Last week, it had been thought that Granada chief executive Steve Morrison would be the loser in a potential combination of the two companies.
Meanwhile, bidding for ITV Digital's stuffed knitted mascot Monkey heated up over the weekend with news that Clear Channel Entertainment, the events and entertainment group, has offered £100,000 to buy the character from ITV Digital's administrator Deloitte & Touche.
Clear Channel said it wants to turn Monkey into the star of films, books and DVDs.
Deloitte, which is currently involved in a custody battle with Monkey's creator advertising agency Mother, has set Friday as a deadline for bids for the rights to the toy mascot.
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