Fullkrug, 33, joined West Ham following an impressive season at Borussia Dortmund for a reported £27 million back in the summer of 2024.
The former Germany international really struggled to adapt to English football and scored three goals in 29 games, adding to the long list of failed West Ham striker signings.
According to BILD, Fullkrug has now agreed personal terms with newly promoted Serie A side Venezia, but the move has been blocked over the price.
He is currently not training with the team, but is keeping fit individually and is still expected to leave the Championship side this summer.
Fullkrug has a history in Serie A having bagged a shock loan move to AC Milan for the second half of last season, where he also failed, scoring one goal in 20 games.