The unsettled Uruguay striker went public with his grievances after a second bid of £40million plus £1 by Arsenal, which they thought should have triggered his departure, was rejected by the Anfield club in July.
Liverpool have always maintained there was no release clause as such - only a requirement to notify the player and begin negotiations should they wish.
And Gerrard does not think a move to another Barclays Premier League outfit would be right for Suarez, who has since rejoined the first-team squad after apologising for his behaviour over the summer.
Quoted in several national newspapers, the England skipper said: "I didn't ever think Luis would leave - well, not to another English club anyway.
"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."
He continued: "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.