Le 10 Sport says both sides have an interest in the playmaker, but any move hinges on the rehabilitation regarding a knee injury he sustained last season.
The Spanish giants tried to sell the 28-year-old in the summer of 2019 but were unable to find a buyer and he ended up spending the season on loan at Bayern Munich.
Despite winning the treble, Coutinho's game-time in Bavaria was limited by injury and the Bundesliga giants decided against signing him permanently following his bit-part role.
Given a second chance at Camp Nou by Ronald Koeman last summer, Coutinho started the season well, but has not played since December due to injury.
Reports in Spain have indicated over the last few months that Barca will look to sell Coutinho this summer as new president Joan Laporta plans a squad overhaul.
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