The Brazilian, who left Anfield for the Nou Camp in January, scored five goals in five group stage games for Liverpool earlier this season.
The Reds are through to the Champions League semi-finals after a 5-1 aggregate win over Man City in the quarter-finals.
UEFA rules mean he was ineligible to feature for Barcelona in their quarter-final loss to Roma.
Regulations also state, however, that should his former club triumph in Europe they will receive 40 Champions League medals.
Coutinho could, therefore, still receive one of those winner’s medals for his contribution to Liverpool’s success, though it is understood Liverpool manager Jurgen Klopp would have the final say on the decision.
Former Liverpool defender and Sky Sports pundit Phil Thompson believes that it would be “wrong” to award Coutinho a winner’s medal while he’s no longer at the club.
“He left Liverpool to go to Barca knowing he wasn’t going to play Champions League football at Barca,” he said. “Listen I got a medal in 1977 for Liverpool because I played until the semi-final, I don’t count it as a winner’s medal.”
“I’d like to think if we do go on to win it that he says no I don’t deserve it, I don’t care it’s wrong.”