According to a report in The Observer at the weekend, investors see Dyke as a white knight who could save broadcaster from falling into US hands.
Dyke is reported to have told friends that he is "very interested" in taking over from the embattled Allen, who has been under pressure since the merger of Carlton and Granada.
Earlier this year, it was reported that powerful City fund manager Anthony Bolton had spoken to Dyke about a role at ITV.
It was Bolton, dubbed the City's "quiet assassin", who last year brought down Carlton chairman Michael Green and had him removed as chairman-elect of ITV.
Since then, he has been putting pressure on Allen and is understood to want to replace him as chief executive with Dyke.
The pressure on Allen comes as ITV plays down reports that it could face a shortfall in advertising revenues of £100m because of falling audience share.
ITV faces the prospect of losing out on revenues because of Ofcom's Contracts Rights Renewal remedy. This gives advertisers the right to pay less for advertising if audiences fall and the figure being suggested is as much as a 3.5% drop in ITV's advertising revenues in 2005, leading to a shortfall of £100m.
ITV has denied this, saying that the figure of £100m was overblown and that, with a decline in audience share from 42.7% to 41.9%, the shortfall was more likely to be £30m.
Investors are concerned that falling audiences figures and share price could lead to ITV being snapped up on the cheap by a US media giant.
Investors, including Deutsche Bank's asset management arm, want to see Dyke brought in so that he can reinvigorate ITV and double its share price in the next 18 months.
One analyst said told The Observer: "If Dyke was appointed tomorrow, I reckon that the shares would go up 30%."
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