Goal exclusively revealed that Arsenal had 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.
But his current team-mate and England captain Gerrard thinks the 26-year-old should show the club loyalty, and remain while they attempt qualify for Europe's elite competition for themselves.
|2/9||Liverpool are 2/9 with William Hill to win no trophies in the 2013/14 season
"Alongside Gareth Bale, Luis is the third best player in the world after Lionel 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.
He added: "This club needs to make one or two big signings if we are to compete for the top four – and keep Suarez.
"Of course, we're slightly behind the big three [Manchester United, Manchester City and Chelsea], who are powerhouses at the moment.
"Once in the Champions League, Gerrard insists there is no better experience than playing for Liverpool on the biggest stage.
"If Luis experiences Champions League football here he'll love it," he continued. "They'll be some of the best nights in his career. To play Champions League football in front of our fans is special. It's an awful lot bigger than doing it at other clubs.
Gerrard admits that his club's European hopes could hinge on whether Gareth Bale makes a world-record move to Real Madrid, but is adamant that Liverpool have just as a good a chance as Arsenal of netting a top-four finish.
"I don't think Arsenal is a step up. Us, Arsenal and Tottenham are fighting for one of the Champions League places. In an ideal scenario we keep Suarez, make one or two more signings and Tottenham lose Bale.
"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," he added.