Despite sticking by Suarez through some difficult times, Liverpool risk losing the Uruguayan in the summer if they cannot deliver UEFA Champions League football.
And the Reds skipper is urging his team-mates to meet the ambitions of their star striker by fighting their way up the table.
"Hopefully, we can put a fight on for him between now and the end of the season to finish fourth and we make a decision for him," said Gerrard.
"Only he knows what his ambitions and dreams are. Luis deserves to be in the Champions League - everyone has to admit that.
"Outside of Leo Messi and Cristiano Ronaldo, I'll argue he's as good as anyone else.
"He's probably the best player I've played with and I've played with some top players in my career."
Gerrard himself has been receiving plenty of plaudits after being heralded as Liverpool's "greatest player ever" by team-mate Jamie Carragher when honoured by the Football Writers' Association at a gala tribute dinner.
Carragher is in no doubt of Gerrard's place among Anfield legends.
"I think we are in the presence of the greatest player ever to play for Liverpool," said Carragher.
"People will say I am biased because we are good friends and because of the trophies we have won together, but it is a fair accolade to give him.
"There are guys like Kenny [Dalglish], Graeme Souness, Ian Rush, all world-class players, but the difference was they were in a world-class team - and Stevie has not played in a world-class team."
Carragher added: "Stevie's one strength is he has no weakness, he can run, tackle pass and score goals.
"Football is a team game, but special players do special things at special times, and that is Steven Gerrard."