Suarez has expressed a desire to leave the club after they failed to qualify for the Champions League, with Arsenal and Real Madrid linked with a move for the Uruguayan.
But Gerrard, who has remained a one-club man despite interest from across Europe, wants his team-mate to demonstrate a similar level of loyalty.
The 33-year-old also rejected the possibility that Suarez would join a Premier League rival.
"It's very important (he stays)," he said. "He's one of the best players in the world (and) if I can use my influence to try and make him stay, of course I will do.
"I love playing with him, I don't want him to go.
"At the moment, I don't know what's going to happen over the next couple of weeks, but I'm really confident he won't be going to anyone else in England."
Gerrard was speaking ahead of England's international friendly against Scotland at Wembley on Wednesday, and the national team skipper insisted that his side were fully committed to securing a victory against their fierce rivals.
"We're expecting a quick start, a high tempo," he added. "It's important we go in feeling confident, it's an important game for us.
"We want to win the game; there will be no holding back because it is a big game."
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