The European Union's former Brexit negotiator, Michel Barnier, said today he was setting up a political faction under the name "Patriot and European".
It has fuelled rumours that he was mulling a possible bid in next year's French presidential election.
"I am available to work with all those who want it under the banner of 'Patriot and European', so as not to leave this theme to others," Mr Barnier told centre-right politicians in a closed-door meeting, according to a participant.
The faction was presented as a "working group" within the centre-right Les Republicains party, the participant said.
Mr Barnier's office did not return a request for comment.
More than a year before the first round of the 2022 presidential election, none of the former mainstream centre-left and centre-right parties, who were shut out by centrist Emmanuel Macron's victory in 2017, have chosen a candidate.
Each camp is abuzz with rumours, and sources on the right cite Mr Barnier, along with ex-ministers Xavier Bertrand and Valerie Pecresse, as well as senator Bruno Retailleau, as possible candidates for Les Republicains.
A possible bid by Mr Barnier, a 70-year-old former French foreign minister, is being closely watched by Mr Macron's camp, as he would eat at the pro-European, centre-right electorate the president is targeting.
"There's a Biden moment. Grey hair could become fashionable," a minister said on condition of anonymity, when asked about Mr Barnier.
Mr Barnier said on French radio in December he saw himself serving his home country in some capacity following his work on negotiating Britain's exit from the EU, without elaborating.
A diplomat in Brussels said he was "actively evaluating his chances" for the presidential election, which current polls show Mr Macron and far-right leader Marine Le Pen as likely to reach the second round.
On the left, sources in Mr Macron's government say Paris mayor Anne Hidalgo is also mulling a presidential bid. The Spanish-born 61-year-old Socialist is no longer ruling out running for president in interviews.
"Hidalgo is going to go for it. Her team is ready for battle," one official said.