Barcelona beat Villarreal 2-1 on Sunday night to go level on points with Real Madrid.
With Atletico Madrid losing against Athletic Bilbao, the top spot is only two points away now with a game in hand.
Griezmann knocked in both goals in a crucial tie as Barcelona still have six games to work their way to the top.
“We all want to win LaLiga,” Griezmann said. “There are four teams that are fighting and trying to win all our games.
“It won’t be easy, but we have the team to do it. [The title favourites] are always the ones who are top of the table. Atletico are having an incredible season and we’re doing our best to be champions. We have it in our hands. We just have to win all our games.”
Griezmann has now scored four goals in three games, thriving alongside Lionel Messi.
“I try to get in between the centre-backs, get into space, make space for my teammates…” Griezmann added. “It’s not my natural position, but it’s an honour to be at Barcelona, with these teammates and doing my best, sometimes with goals and other times with assists.”