The Telegraph says two Premier League clubs are weighing up bringing Greenwood back to England.
In England, there is a belief Greenwood can make a return after assault charges were dropped against him two years ago.
Greenwood has rebuilt his career over the past two seasons, first with Getafe on-loan from Manchester United, before being sold to OM last summer.
In France, Greenwood has scored 19 goals for OM across all competitions in career best stats. And his OM coach Roberto de Zerbi believes there's more to come.
A Marseille legend
He said: "Greenwood is a natural talent. All the credit goes to his mother and father. And I'm here to help him become more complete.
"When he needs a hug, a word of support, I gladly give it. And when I need to push him to give more, I have to do that too because that's my job.'
"I would especially like to help him be remembered, in this stadium and by these supporters, as one of the greatest players to have played here at the Velodrome.
"There have been so many great players here, but I think Greenwood has the qualities to be remembered that way. And I'm trying to help him progress."