The Belgium international has been linked with a move to San Siro throughout the transfer window, with the Nerazzurri keen on partnering new signing Radja Nainggolan with his compatriot next year.
It was claimed that a £20m fee had been agreed between both clubs for the move to go through. However, the Daily Mail confirm that Dembélé will instead see out the remainder of his contract despite falling down the pecking order under Mauricio Pochettino.
The 31-year-old made an impressive 39 appearances across all competitions last season acting as the engine of Spurs' midfield, but saw less game time as the campaign went on, with manager Pochettino instead putting his faith in the defensive Victor Wanyama.
Dembélé, an Eredivisie winner from his time with AZ Alkmaar, has spent six years with Tottenham following a £17m switch from London rivals Fulham.
The experienced midfielder has gone on to make 236 appearances for the club since his arrival in 2012, scoring 10 goals and claiming 11 assists.
Dembélé has earned a reputation in the Premier League for being one of the toughest players in the top flight, but it is suggested that the physicality of the division is becoming too much for the left-footed midfielder.
Instead of securing a move this summer, however, it appears that Dembélé is happy to see out the remainder of his contract in a bid to keep his options open over his next move in 2019.