The website claim Tottenham are considering making an offer of €26 million for the 23-year-old.
Destro has four goals in seven Serie A starts this season, but is not a regular starter for the side, despite a superb end of season run a year ago which saw him net 13 goals in 15 starts.
The report goes on to state Destro would consider saying yes to a move to Tottenham, should they make a firm offer.
Destro has six international caps to his name with one goal, and has a contract with Roma until 2017.
Check him out in action below...