Maurice Lévy has declared his successor will be an insider and suggested Publicis Groupe is close to naming "him."
Arthur Sadoun, chief executive of Publicis Communications, which runs the group's creative agencies, is regarded as the front-runner to be chairman and chief executive of Publicis Groupe.
Lévy, who has said he will step down by the spring after 30 years in charge, said he wouldn't decide his successor.
"I don't choose him," he said in an interview with Bloomberg in Davos, saying it was up to the board. "We are a public company."
He said the process was "working pretty well" and when asked if his successor will be internal, he said, "unequivocal, yes."
There is speculation that Publicis Groupe will say more about Lévy's successor at the time of its annual results on Feb. 9.
Alan Herrick, who runs Publicis Sapient, has been tipped as a contender or possible co-chief executive of the group alongside Sadoun.
Lévy played down the need for the French ad group to move staff from London because of Brexit, although some financial services clients are likely to move.
"We don't need to do that because we are working locally," he said.
"All our teams are working locally for local clients and there is no reason that we move from London to Paris."
He was a keen supporter of Britain remaining in the European Union before last year's referendum and said of Brexit: "We believe all in all it will be tough, it will be difficult and but it will not have a huge impact on the economy."
Asked how he would advise a business leader at one of his clients to respond if Donald Trump tweeted critical comments about that company, he said: "The first thing to do obviously is to do everything you can to avoid being tweeted [at].
"If there is a tweet, depending on the issue, you need to address it immediately and do not have an argument with the president-elect who will be the president tomorrow."
His advice was try to avoid arguing "in the press" and "negotiate" with the Trump team privately.
Lévy admitted the new president posed new challenges for businesses. "No one knows how to predict the next tweet," he said.