Arsenal bid £40,000,001 for the striker earlier in the summer, which was dismissed by Reds manager Brendan Rodgers.
Gerrard believes that moving to the Gunners would be a sideways step for Suarez, but reveals that there are a few clubs he might consider leaving for.
"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 told The Mirror.
"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."
Gerrard also said that it was important that Suarez did not ruin his relationship with Liverpool's supporters.
He added: "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."
Suarez joined Liverpool from Ajax in 2011.