Griezmann's dream move to the Camp Nou has turned into a nightmare after only registering eight league goals all season.
The Frenchman has only started one of Blaugrana's last four encounters since the restart while he only played a minute against his former side Atletico Madrid on Tuesday.
According to the Mirror, who cited Italian journalist Paolo Paganini, the club are looking to offload Griezmann as part of a swap for either Inter Milan's Lautaro Martinez, Paris Saint-Germain's Neymar or Juvetus midfield duo Adrien Rabiot and Douglas Costa.
Griezmann's current position in the squad was not helped by Barcelona manager Quique Setien's comments after the draw with Atletico.
"I understand it's tough for Griezmann to come on when so little time left," he said, according to Goal.
"I will speak with him tomorrow; I won't say sorry because (it's about) decisions.
"But I understand he may feel bad, and I feel bad for him because he's a great person and professional.
"It's difficult to put him on without destabilising the team."