Correa joined Inter in August 2021 from league rivals Lazio on a one-year loan with an obligation to buy. He helped both teams to the Italian Cup and Italian Super Cup trophies.
He also helped Inter reach the Champions League final last season where they lost to Manchester City.
The 29-year-old Correa made his Argentina debut in June 2017 in a friendly win over Brazil and has 19 caps, winning the Copa America in 2021 and the ‘Finalissima’ in 2022 against Italy.
He was called up by manager Lionel Scaloni for the 2022 World Cup in Qatar but dropped from the squad due to an injury five days before the tournament started.
Marseille are sixth in Ligue 1 with four points from two games ahead of hosting second-placed Brest on Saturday.
(Reporting by Anita Kobylinska in Gdansk; Editing by Ken Ferris)