Dow Jones newswires cite sources close to De Pouzilhac saying he will step down from his executive role at Havas, but stay on in an advisory role at the company.
Havas refused to comment on the speculation. The company's board of directors is due to meet next Tuesday.
The crisis has been sparked by the victory last week of Vincent Bollore in his attempt to take four seats on the board of Havas, the company in which he controls a 26% stake. De Pouzilhac had long opposed Bollore's move and it had been widely thought that he would step down if Bollore was successful.
Following the meeting last Thursday, Bollore said De Pouzilhac was welcome to stay, and De Pouzilhac emailed Havas staff on Friday to say that he would be putting his heart and his energy into running the company.
However, since then he has met with Bollore, who has been reported in the French media as saying he was a "bit surprised" that De Pouzilhac had not resigned.
Dru has been chief executive of TBWA\ since 2001, and is credited with transforming a disparate group of agencies into a unified global network.
He came up to senior management from the creative side of advertising, having been made executive creative director of Dupuy-Compton, the agency which became Saatchi & Saatchi, in 1972 when he was just 25.
The Wall Street Journal reports that he is the preferred candidate for the job, but that he has not decided yet if he will accept. At age 58, there has been speculation that he will soon retire.
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