Arsenal recently tabled an improved £42 million offer for the Uruguay international, who is becoming increasingly unsettled at the club with Arsene Wenger's side ready to offer him Champions League football.
However, Gerrard thinks the 26-year-old should only leave Liverpool if either Barca or Madrid come knocking.
|2/9||Liverpool are 2/9 with William Hill to win no trophies in the 2013/14 season
"He’s a South American. He’s good enough to play in either of those teams. From a family point of view, it’s where they all want to be. Javier Mascherano, Xabi Alonso, some of the top players I’ve played with – their dream was to play for Real or Barcelona.
"If I was him I would wait for one of those two clubs because I think he’s good enough to play for them.
"I don't think Arsenal are a step up. Us, Arsenal and Tottenham are fighting for one of the Champions League places.
"I don't want to disrespect Arsenal. They're a wonderful club with a manager who I've an awful amount of respect for and they have talented players throughout the team.
"But so have we. We’ve got just as good a chance of achieving things as Arsenal have."
Gerrard then went on to state that he feels Suarez is on the same level as Gareth Bale and only just behing stars such as Lionel Messi and Cristiano Ronaldo.
"Alongside Bale, Luis is the third best player in the world after Messi and Cristiano Ronaldo. Luis and Bale are the two hottest properties out there at the moment.
"When you're in that position, you’re going to get all kinds of teams wanting to pull you away, especially when you are at a club not in the Champions League.
"It's nothing to do with the British media [criticising Suarez]. Knowing the guy as I do that’s probably the thing on his mind: wanting to be in the Champions League."
The midfielder believes Liverpool need to invest in a couple more signings this summer and then they will be in a position to challenge for a place among the league's elite.
"Of course, we're slightly behind the big three [Manchester United, Manchester City and Chelsea], who are powerhouses at the moment.
"This club needs to make one or two big signings if we are to compete for the top four – and keep Suarez."