The England international and 26-year-old South American have been in devastating form since Suarez returned from a 10-game ban for biting Chelsea defender Branislav Ivanovic in April.
“It’s great to play with him, we give defenders problems and we both play differently, so it’s good to have a strike partner you can bounce off,” Sturridge told talkSPORT.
“It’s going to great for him and everybody wants him to stay and it’s up to Luis to decide what he wants to do.
“We as a club, the fans and the players, everybody wants him to stay, but if Luis wants to decide it’s best for him to move on then that’s the way it’s got to be. But I think everybody wants Luis to stay and I’m sure that he will.”
Sturridge has scored 18 goals in 23 top-flight appearances following his £12m move to Liverpool from Chelsea in January.
MORE: The latest football news