The Reds have stuck by Suarez through some tough times, but the Uruguayan may nevertheless decide his future lies elsewhere should the Anfield club fail to book their place among Europe's elite.
"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," Gerrard was quoted as saying in The Sun.
"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."