They however face an difficult battle, with Wimmer establishing himself as a vital player in Tottenham's squad over the course of the season.
Wimmer is Tottenham's third choice centre-back, but put forward a convincing argument that he deserves a regular starting spot, even if it will be tough to break up the Toby Alderweireld and Jan Vertonghen partnership.
Roma want to sign him as a potential replacement for Antonio Rudiger, who is being touted around for a switch this summer.
Interest in Wimmer is understandable, but Roma have no chance of convincing Spurs to sell at just £5.5 million, a fee only narrowly above the amount Spurs paid to sign him from Cologne last summer.
Their only chance would be if the Austrian expressed frustration with his role, but Wimmer appears happy at Tottenham and is willing to fight for his place.
Reliable centre-backs are hard to find, and Wimmer could play a vital role next season once again with Spurs aiming to compete in both the Premier League and Champions League.
If Roma want to sign a centre-back from Tottenham, they may be more successful targeting Federico Fazio instead.