Adem Ljajic has failed to agree a new contract with Fiorentina, so Roma joined Milan, Tottenham and Southampton with offers.
The Serbia international met with Viola directors at their headquarters on Friday afternoon, but left without securing an extension to the deal that expires in June 2014.
President Andrea Della Valle noted on Thursday that he would be sold if there was no new contract and there was “not much chance” of him staying.
Milan have long been interested in Ljajic, even though their initial €9m offer was rejected, and remain the favourites.
It was reported Atletico Madrid made a proposal, but the forward turned down that alternative.
Over the last few hours Roma have emerged as new contenders for Ljajic’s signature, as he would be a valid replacement should Erik Lamela join Tottenham for €35m.
Other options are Spurs, Southampton and Schalke 04, though the player seems eager to remain in Serie A.
According to Sky Sport Italia, Ljajic will give Fiorentina his definitive answer on Tuesday morning after their Serie A match against Catania.