The Corriere dello Sport and Coeur Marseillais maintain the proposal on the table is worth €10m.
However, La Dea are requesting a minimum of €15m to part with the Colombia international.
The 31-year-old was one of the most expensive ever signings for Atalanta when joining from Sevilla for €21m in the summer of 2019.
A departure seems likely because his contract is due to expire in June 2023 and the club has failed to qualify for Europe after three consecutive Champions League campaigns.
Muriel scored 14 goals and provided 10 assists in 39 competitive matches for Atalanta this season, where he was given more responsibility due to a long-term Duvan Zapata injury.
He didn’t always deliver, struggling when starting a match compared to his previous super-sub status coming off the bench to run at tired legs.
— TuttoAtalanta.com (@tuttoatalanta) June 21, 2022