The defender is widely tipped to leave Tottenham Hotspur this summer after failing to agree a new contract with the club.
This would bring an end to his eight-year association with the North London side.
According to the report, the Italian giants have offered Vertonghen a two-year contract with the option of a third.
Roma are keen to bring in an experienced defender this summer with Chris Smalling set to return to Manchester United.
The former England defender has enjoyed a successful campaign with the Italian side, however a move for Vertonghen could prove to be a more cost effective solution give his contract situation.
GIVEMESPORT'S Phil Spencer says...
The writing certainly appears to be on the wall regarding Jan Vertonghen's future.
The defender has undoubtedly been a superb servant for Tottenham Hotspur after spending eight years with the club.
But with his contract coming to an end it seems like the time to move on.
Realistically, this will be the Belgian international's last opportunity to earn a big contract in his playing career, and that will surely be factored into his decision.
After eight years it's also understandable to want a new challenge, and that's something he'd certainly get with Roma.
A deal is far from complete, but it certainly seems like a move that could be finalised sooner rather than later.News Now - Sport News