Dembele joined the Hoops from Fulham last summer for merely £500,000 and went on to score 32 goals in his debut campaign in Scottish football.
The French striker, who was instrumental to help Brendan Rodgers’ side remain unbeaten in completing a domestic treble this season, soon became a fan favorite at Celtic after netting an impressive hat trick in his first game against arch rivals Rangers.
Premier League champions Chelsea and Borussia Dortmund are also thought to be interested to sign Dembele but AC Milan have moved quickly to strike an early deal for the 20-year-old.
The Rossoneri have began a major squad overhaul following a change in club ownership with the new Chinese owners determined to improve the club’s current sixth-place finish in the Serie A.
AC Milan have already signed Mateo Musacchio and Franck Kessie while club manager Vincenzo Montella has also penned down a new contract to keep him at the club until 2019.
Dembele’s current contract with the Hoops runs until 2020 and any transfer deal for the PSG youth academy product is likely to cost in excess of £30 million this summer.