The Uruguayan striker was informed by new manager Ronald Koeman that he is no longer needed at the Camp Nou after six years with the club, according to RAC1.
Spanish publication Sport have now reported that the Catalan giants are lining up Lyon's Dembele for a switch ahead of the 2020/2021 season.
The Frenchman has made a name for himself in Lyon since leaving Scottish giants Celtic in 2018, after registering 44 goals and 13 assists in 92 appearances.
Barcelona may well get their reported target after Lyon director admitted the club might need to sell a few big-name players following their UEFA Champions League exit earlier this month.
"If we continue the way we have, we will be back in the Champions League very soon," he said, as per the Sun.
"Players will be leaving, like Houssem Aouar and Moussa Dembele, but I'm not worried. We want to secure Champions League football next season."