However, he accepts next summer could be a different matter if the Reds have not qualified for the Champions League.
The England midfielder admits he spent much of pre-season wondering whether the Uruguay international would remain at Anfield, especially after Arsenal's £40,000,001 bid and the player himself claiming the Reds had reneged on a deal to allow him to join a Champions League side.
Suarez has since revealed Gerrard's words of persuasion were a significant factor in him not pressing further for a move.
Liverpool's captain said he is not as concerned about the coming transfer window as he was during the last one but admits familiar problems may resurface next summer, especially if the Reds do not re-establish their place in the top four.
"I don't feel like that about January... January will be different because I think Luis is committed," he told ESPN.
"I think he is happy. I think he is pleased with the decision he has made to stay around.
"He is in good form. The team are playing well so I think January won't be a problem.
"But come the summer, I think depending how Liverpool have done will determine what goes through Luis' mind.
"He is the key. His goals, his performance and his form will be the key whether we finish in the top four or not."
Suarez scored 30 goals in all competitions for the Merseysiders last season and he has already found the net six times in five league matches in the current campaign after missing the start through suspension.
That is why Gerrard rates the 26-year-old as the best player he has played alongside.
"Yes. Simple. He's out on his own," added the midfielder.
"The only player who comes close to producing what Luis produced in a red shirt is Fernando Torres but Luis just pipped him for me."
Since returning from his ban, carried over from the previous season for biting Chelsea's Branislav Ivanovic, Suarez has shown no signs of unhappiness over what happened during the summer.
To the contrary, he has frequently made encouraging noises about how happy he is and how well the campaign is going with Liverpool third in the Premier League, five points behind leaders Arsenal.
"We're doing well right now but we need to carry on that form into the Christmas period," he told Match magazine.
"I think our best is yet to come, which hopefully means well for the end of the season and our chances of making next season's Champions League. That's one of our aims.
"It's good to be playing well and contributing with goals, but the most important thing is getting three points every week.
"I wouldn't be scoring without the help of my team-mates, so thanks to them."
Fellow striker Daniel Sturridge, who himself has scored eight times in 10 league matches, recently described his partnership with Suarez as "a beautiful thing".
Suarez repaid the compliment by saying: "He's a fantastic player and strike partner and we get on very well.
"I hope we continue to score goals and win more awards, but it doesn't matter who gets the goals or awards as long as we keep winning games."