Greg Dyke, the former BBC director-general, is leading the list of names that also includes the outgoing Ofcom chief executive Stephen Carter and Channel 4 chief executive Andy Duncan.
This morning, shares in ITV climbed to just shy of 100p, up 0.76% to 99.75p, having fallen as low as 94p last week.
It has been speculated that Allen's reign at ITV could come to end as early as August when the broadcaster announces its interim results.
Investors are said to have met with Sir Peter Burt, the ITV chairman, to press for change at the top of ITV.
The broadcaster intensified media speculation yesterday by failing to issue a statement to clarify the situation, following weekend reports that Allen was set to depart the underperforming ITV, which caused its share price to sink below 100p.
News that Allen might be set to announced lifted ITV's shares slightly to 99p, a rise of just under 3p, but this morning they had fallen back further to 98.5p.
Spread betting firm Cantor Index issued its list of favourites for the job, putting Dyke at the top.
In March, he led a £1.3bn takeover deal of ITV, backed by investment bank Goldman Sachs and private equity firms, which failed to win the backing of the ITV board.
Despite this failure, Dyke is seen as someone who could inject new life and direction into ITV, which having had a poor World Cup is currently dealing with its flagship summer reality show, 'Love Island', faring badly in the ratings.
Some institutional investors, including Fidelity, which with a 13% stake holds some sway over ITV and was responsible for ousting chairman designate Michael Green at the time of the Carlton/Granada merger to create ITV plc, are backing Dyke.
However, many are tipping Carter for the job. He leaves media regulator at the end of July and has previous experience running cable firm NTL. Prior to that, he ran WPP Group advertising agency JWT.
Others in the running for the ITV chief's executive job are: former BSkyB chief Tony Ball; former Channel 4 chief executive Michael Jackson; and Five chief executive Jane Lighting.
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