However, a serious ankle injury has limited the French international to just two Ligue 1 appearances this season.
And with OM in financial trouble and fined by UEFA for breaching FFP rules, they will have to let some big earners go.
In the summer of 2018, club president Jacques-Henri Eyraud was demanding over €80m for Thauvin during his best form.
But two years on and the situation has changed, with Thauvin out of contract in a year’s time.
Thauvin said in April that he would be staying at Marseille next season but OM have invited offers with a tempting price-tag.
Head coach Andre Villas-Boas has been determined to use Thauvin next season and could have a say in the matter.
However, should an offer of around €20m be lodged for Thauvin, Marseille will be inclined to accept it.