However, the news of the bid has angered the Ukraine side's head coach Mircea Lucescu, who insists the player will not be leaving in this transfer window.
West Ham are also thought to be tracking the experienced 31-year-old, who is the captain of the national side, along with Turkish outfit Besiktas.
It now seems as though the player, who has plied his trade at Donetsk for the past 10 years, will remain at the club for now.
Lucescu told French website Sport365.fr: "Marseille have made an offer for Razvan. I have spoken with the Marseille president, Vincent Labrune.
"If they really want him, they would have made an offer at the beginning of January.
"I cannot let him go just before the end of the transfer window because I can't find another left-back so soon."