The Uruguayan striker, 25, was embroiled in controversy in 2011 with the infamous race row involving Patrice Evra and is continually accused of diving - making him a regular target for boo-boys.
Suarez has even won enemies in non-league football having ousted Mansfield from the FA Cup courtesy of a goal before which he handled the ball, but Reds team-mate Leiva is hoping he can shrug off the criticism.
Leiva told the Daily Star: "It doesn't seem to worry him too much. I think if he was worried it would have affected his performances on the pitch. If in the future he will get tired of it, we don't know.
"We hope he doesn't and people will start to give him some credit. At the moment we can see he's very happy. He's enjoying his football here.
"It could be too much for him but it could as well be a motivation just to keep going. That's the strong character that he has. And maybe instead of being a negative thing it could be a positive one
"A lot of players like to go and get boos and that gives them an extra incentive. I don't know how Luis feels - but it doesn't seem to bother him too much.
"So we hope he keeps playing well and stays at Liverpool because he's a special player and an important one for the future. I just think he copes very well with that.
"If people still criticise him and he keeps scoring goals I don't think he will be too worried about it."