Corriere dello Sport report that Gasperini has a "real obsession" with signing the 24-year-old Englishman and has gone as far as attempting to speak directly with the player to sell him on the AS Roma project.
The initial offer from Roma is expected to be in the region of €40 million including bonuses — a figure the club's own hierarchy acknowledges will not be sufficient.
Olympique Marseille are holding firm at between €50 million and €55 million. The gap is complicated further by a 40 per cent sell-on clause that Manchester United retain from the original transfer, meaning any fee paid to Marseille is effectively discounted before the French club sees the full benefit.
Greenwood scored 26 goals and contributed 11 assists in 45 appearances for Marseille this season — one of the most productive campaigns by a forward in Ligue 1 this year. The numbers have earned him Ligue 1 Player of the Season consideration and transformed his market value since arriving in France for €26 million in 2024.
Roma's interest is not new. Contacts between Greenwood's representatives and the Giallorossi have continued steadily, with Corriere dello Sport reporting that the player's father has also been in direct communication with the Italian club. Greenwood is understood to be open to the move.
The complication is the fee. Roma's opening bid will be approximately €10 million short of Marseille's minimum figure, and Gasperini's new sporting director Tony D'Amico — set to take office this week — will need to negotiate the gap quickly.
Marseille face financial pressure from France's football financial watchdog, the DNCG, and need to raise funds by the end of June. That urgency cuts both ways.
Greenwood's personal terms are not in dispute. Corriere dello Sport report he is seeking a salary of no less than €4 million per year plus bonuses — a package that across a five-year contract would approach €100 million gross for Roma.
The deal has shape. It has momentum. What it still needs is a number both clubs can accept.