The 26-year-old is currently serving his suspension for biting Chelsea defender Branislav Ivanovic in April and will not return to first-team action for the Reds until late September at the earliest.
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"I don't think that what's happened to Luis will affect him much in terms of his future," Gerrard told the Liverpool Daily Post.
"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."
Gerrard also says that Suarez accepting his ban was the correct decision, and that the striker will want to atone for his mistakes next season.
"Luis has done the right thing by apologising and taking his medicine," Gerrard added.
"He's really unhappy he can't help the team, and he was really down when the ban came through. But once he is back from his ban we will be the ones that benefit.
"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."