Marca says Barca are set to bid for the out-of-favour Belgian as a replacement for Jasper Cillessen.
Mignolet is now unlikely to play for the Reds again after Alisson completed his £68million move to Anfield.
Despite his numerous recent blunders - including two in the Champions League final - Loris Karius is also above Mignolet in the pecking order.
The Belgian stopper would not be signed as first-choice at Barca though - with Marc-Andre ter Stegen holding that mantle.
However, Barcelona see him as a fine understudy to the German with Cillessen on the way out.