Since 2020, Coeure, 52, has headed the Innovation Hub of the Bank for International Settlements, a newly created body which he moved to after eight years at the ECB.
Coeure would replace Isabelle de Silva, whose five-year mandate as head of the competition watchdog ended in October and comes as the regulator is due to make a ruling on the proposed merger of France's number one and two TV networks TF1 and M6.
Coeure trained as an economist at France's prestigious Polytechnique university and earned a degree in Japanese before holding various positions at the French treasury, ranging from chief economist to G8 finance sherpa and head of the public debt management office.
He later joined the ECB's Executive Board where he was in charge of market infrastructure and seen as one of then ECB chief Mario Draghi's closest lieutenants.
While a widely respected macroeconomist, Coeure's approach to regulating big tech and companies is largely unknown.
De Silva's tenure at the watchdog was marked by hefty fines against U.S. tech giants Apple and Alphabet's Google.
Coeure's name has come up in the past as a possible head of the French central bank.
His appointment to the antitrust watchdog will need to be approved by the French parliament, where Macron's centrist LREM party has a majority.
(Reporting by Sandra Auger and Leigh Thomas; Writing by GV De Clercq, Editing by Tassilo Hummel and Susan Fenton)