According to Sport Bild, Barca enquired about his availability and losing Luis Suarez and Ousmane Dembele to long-term injury and were willing to offer a fee of around €50m.
Director of sport Max Eberl had a think about it but decided against it because Plea was needed to help their bid to qualify for the Champions League.
The Bundesliga club also thought they would find it difficult to bring in a replacement for Plea as such short notice.
Plea is hardly a household name which makes this rumor a bit of a weird one, but he has impressed for Borussia Monchengladbach since joining from Nice in 2018.
The Frenchman scored 15 goals in his first season in Germany and has eight goals and seven assists in 2019-20 so far.
Borussia Monchengladbach are currently fourth in the Bundesliga, and just a point behind RB Leipzig, after 25 games.