Suarez completed a move to Spanish giants Barcelona earlier this month, having helped Liverpool mount a title challenge in his final season at Anfield.
Prior to last term, when Liverpool finished two points behind champions Manchester City, Suarez came close to leaving for Arsenal as he was frozen out and forced to train alone during the 2013-14 close-season.
The Uruguay international eventually agreed a new deal at Anfield in December, only to then join Barca within seven months - a switch Gerrard feels was always on the cards.
"His dream from the first day he came was to play for Real Madrid or Barcelona," the former England captain told The Telegraph.
"Last summer when he was out in the cold and training on his own that's the conversation I had with him. I said: 'Don't go to Arsenal'.
"I would have been really sad and disappointed to see Luis go to Arsenal. With all due respect to them, I said to him that he was too good for Arsenal."
Suarez scored 31 goals in all competitions last season to help Liverpool back into the UEFA Champions League, and was named player of the year by the Professional Footballers' Association (PFA) and Football Writers' Association (FWA).
While Liverpool stood by the player during a series of indiscretions, including biting incidents involving Chelsea's Branislav Ivanovic and Italy defender Giorgio Chiellini at the World Cup, Gerrard understands Suarez's decision to leave.
"I said if you score 30 goals for us and win the PFA player of the year, the press player of the year - I knew he was going to win them - I told him Real or Barcelona will come for you," he added.
"A lot of people might still think he should have given us one more [season], but my big dream was to play for Liverpool, and the foreign players' big dream is to play for Real Madrid or Barcelona, that’s a fact."
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