The unsettled Uruguay striker went public with his grievances after Arsenal had a £40m-plus bid for his services rejected, which the London club thought would trigger a release clause in his contract.
Liverpool maintained there was no such clause, and Suarez eventually returned to the first-team squad after apologising for his behaviour.
He remains on the sidelines because of the 10-game ban meted out for biting Chelsea's Branislav Ivanovic last season, but Gerrard will be happy to welcome him back later this month to boost their bid for a Champions League place, which he hopes could keep Suarez at the club even longer.
"I didn't ever think Luis would leave - well, not to another English club anyway," Gerrard is quoted as saying in the Sunday newspapers.
"I don't want to disrespect Arsenal, because they are a fantastic club, but I don't see joining them as being a step forward for Luis.
"Luis has got to openly admit this club have stood behind him on a couple of massive occasions and they've rewarded him with new contracts as well.
"I think he's got to stop and realise that the club have been fair to him. He is at the right age (26), he is going to be fantastic for us if he stays for another year.
"There are only really two or three clubs he should leave this football club for if he is taking a step forward.
"If we don't qualify for the Champions League this season he can go to Real Madrid, Barcelona or Bayern Munich - and he can go with his head held high.
"The one thing I can assure you - it's not about money with Luis Suarez.
"I understand we're a little bit off the Champions League here at the moment, but I think he would ruin the relationship he has got with the supporters here if he went to another English club.
"I saw what happened to Fernando Torres. I didn't want Luis to make the same mistake and that's the advice I gave him. He'll have another chance to move forward to a club that he deserves to be at."