United wanted Dembele, 23, on a loan deal but Barcelona insisted he renew his contract before such a move.
Dembele is already holding talk with the Italian side about joining next summer or in 2022 when his Barca contract ends.
For now, Dembele will focus on trying to make his fourth season with Barcelona a success.
In the opening three games of Barcelona’s season, Dembele has appeared for just 20 minutes as a substitute against Villarreal.
Ronald Koeman did not make use of him at all in Barca’s games against Celta Vigo and Sevilla.
The ambidextrous winger has struggled since his €100m-plus move from Borussia Dortmund in 2017.
Barcelona are reportedly furious at Dembele for turning down a move to United.