A report in the Guardian this morning says that ITV chairman Sir Peter Burt has held a meeting with Dyke said to have "gone well", which has refuelled speculation that Allen's position might not be safe.
In February the influential City fund manager Anthony Bolton was reported to have been courting Dyke, raising the possibility that he was being lined up for a pivotal 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.
Bolton is no fan of Allen, who is unpopular with shareholders, and is widely thought to want to see him replaced with Dyke.
Bolton was said to have spoken with Dyke, who was forced to quit as director-general of the BBC in January following the publication of the Hutton Report, by telephone as well as praising him in meetings.
If he was to take the job at ITV it would see the former BBC chief turn the tables on Allen who removed him as chief executive of London Weekend Television when Granada took over the ITV franchise in 1994.
There has been constant speculation that Allen would be replaced since Green was ousted last year.
When Sir Peter Burt was confirmed in February as the new chairman of ITV, he was prompted to say that Allen was safe and that he had no intention of leading a campaign to oust him.
Sir Peter, the former chief executive of the Bank of Scotland, said he would not have taken the job if it involved getting rid of Allen. "I would not have accepted the job if my first task had been to get rid of the chief executive. That would have been absolutely daft," Sir Peter said.
However, since leaving the BBC Dyke has been linked with a number of jobs, including a return to his old job at the BBC following the appointment of Michael Grade as the broadcaster's new chairman.
It was suggested that Dyke was being urged by close friends to apply to Grade and make a welcome return to the BBC.
Dyke has also been linked with the chairmanship of the Television Corporation. The job has been thrown open after Grade resigned from the independent producer following his appointment as BBC chairman.
Television Corporation is behind programmes such as 'Question Time', Channel 4's cricket coverage and the BBC's horse racing coverage.
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