Suarez received a 10-match suspension for biting Chelsea defender Branislav Ivanovic, which will see the Uruguay forward absent from his side's squad until September.
However, while Gerrard has admitted that Suarez was right to accept his punishment, the England skipper believes that his teammate will be eager to atone for his mistake next season.
The 32-year-old told the Liverpool Echo: "Luis has done the right thing by apologising and taking his medicine. He's really unhappy that he can't help the team, and he was really down when the ban came through.
"Luis will want to make it up to the club and the team that he has been out for so long. He will be desperate to atone for that. I don't think that what's happened to Luis will affect him much in terms of his future. Maybe one day we will have to accept that Luis wants to move on, and that will be his decision.
"But I don't see any signs of it at the moment. Luis has been really happy here at Liverpool and he seems settled here. I don't see him wanting to leave right now."
Suarez has been linked with a move to Bayern Munich during the summer.