Messi, 32, has managed to make just a single start across all competitions in 2019-20, with a calf strain suffered in early August ruling him out for over a month.
He then sustained a hamstring issue in the 2-1 win over Villarreal, with initial speculation suggesting he could be out for up to three weeks.
But according to reports in the Catalan media, Messi could make his return earlier than expected against Inter in the Champions League on Wednesday, with coach Ernesto Valverde refusing to rule him out.
Griezmann is eager to feature consistently with the Barca talisman having had few opportunities to link up with him.
"He doesn't talk much and neither do I, so it is difficult for us to talk to each other," Griezmann told reporters on Tuesday.
"I have already taken him some mate [tea, a traditional drink of Argentina], so we are going in the right direction.
"He has been injured, so it is difficult to build that connection. I think we are both good people and I'm here to help anyone.
"I am always with him – he trains. He arrives earlier to reinforce his legs and his body. He takes care of himself, but when you enter a sequence of injuries, it is difficult to get out of it.
"He has my support, the support of the coach and that of the team. We are here to help him, so that he feels good. When he is there [in the team], he'll do as he was doing."
Wednesday's match will see Griezmann go up against former Atletico Madrid team-mate and close friend Diego Godin at club level for the first time since the Frenchman left Real Sociedad in 2014.
But Griezmann is confident he can outwit the Uruguayan centre-back.
"In the World Cup [France v Uruguay] it was a special game," Griezmann said. "It will be special to play at home in the Champions League against him.
"He is a great friend and a great example for me. He is my daughter's godfather and I know tricks to catch him if I play and if he plays."