The former Liverpool forward has been deemed surplus to requirements by new Barca head coach Ronald Koeman, who has been tasked with a squad overhaul after the club failed to win silverware for the first time in 12 years in the 2019/20 campaign.
Shortly after his appointment, the Dutchman told Suarez he was not part of his plans moving forward and that his contract could potentially be terminated.
According to reports in Spain, Suarez has already agreed personal terms with the Serie A champions after a meeting with director Pavel Nedved.
Should he move to the Allianz Stadium he would form an attacking partnership with former Clasico rival Cristiano Ronaldo.
Two complications to the move are Suarez's departure from the Camp Nou as well as Gonzalo Higuain.
Both players are unwanted by their current clubs, but compensation will have to be agreed for them to be released from their current deals which have one year left to run.