Griezmann announced his intention to leave Atleti earlier this month, with Barca reportedly in pole position to sign the forward.
Luis Garcia played for both Liverpool and Barcelona during his career, and he feels the World Cup winner would be a good signing for either club.
"I can't wait to see where it's going to end,” said the 40-year-old. “It's true that we know he’s leaving Atletico Madrid, but we don't know anything else.
"So, is it going to be Barcelona or is it going to be United, or Italy? Looking forward, I think it was the moment for him.
“He's been waiting for Atletico Madrid because he knew how important he was for their supporters, but he decided to make the step, and now I’m just looking forward to seeing where he’s going to be playing next year.
"Me? Of course, I'm a Barcelona supporter and a Liverpool supporter, so I would love to have him in my squad. Any of those teams - I'd be happy to see him in.”
Barcelona look set to stick with head coach Ernesto Valverde despite their shock loss to Valencia in the Copa del Rey final, which followed their stunning Champions League exit at the hands of Liverpool.
“I'm happy for that to be honest,” added Luis Garcia, who left Barca to move to Anfield in 2004. “I think you have to give credit to Barcelona.
“It's true that they didn't win the cup, and they couldn't manage to get to the Champions League final, but it’s not easy what Valverde is doing, winning LaLiga and being in (Europe) until the end.
“At the end, only one team can win the Champions League final, so it's very difficult to manage all those kinds of situations.
"I'm happy and looking forward to seeing how he's going to manage for next year and what kind of player he’s going to bring or he's going to let go out.”