The Belgium international midfielder is currently at the World Cup and he has made two appearances for Roberto Martinez's side, helping set up a last 16 match against Japan.
But he will look to sort out his club future even if Belgium progress into the quarter finals at the World Cup, with FCInterNews claiming that Dembélé will hold talks with Inter's sporting director Ausilio in the first week of July.
Dembélé has become well known for being one of the most talented midfielders in the Premier League during an eight-year spell in England, with the first two years being spent with west London outfit Fulham.
The 30-year-old moved to Spurs for £17m in 2012 and Dembélé has gone on to make 236 appearances for the club, reaching double figures in both goals and assists.
But the Tottenham hierarchy are now believed to be lining up a move for Lyon star Tanguy Ndombele - deemed to be a long-term replacement for Dembélé in the heart of their midfield.
However, Spurs' attempts to sign Ndombele could come under threat from their bitter rivals, Arsenal. It has also been suggested in France that the Gunners will turn their attention to the 21-year-old midfielder.
Tottenham are yet to dip their toes in the transfer market this summer, although Netherlands international Vincent Jansen has returned to north London following a spell on loan with Turkish side Fenerbahçe.