AS says BVB have tabled a €20m cash offer for the French forward.
Gameiro is up for sale at Atletico and is also in talks with Valencia. However, BVB's proposal is the superior bid.
Valencia have previously offered €13.5m for the striker.
But Los Che remain favoured by Gameiro, who is reluctant to leave the LaLiga, despite the enthusiastic interest of BVB.