Suarez scored twice in Liverpool's rampant 5-0 victory over Tottenham at White Hart Lane and club captain Gerrard believes it's vital the club qualify for the Champions League to keep hold of the Premier League's leading goalscorer.
Gerrard, who was a special guest on Super Sunday said: "He's relentless, he doesn't give up no matter what the scoreline is, he's always chasing defenders back.
"He wanted a hat-trick today, in the 90th minute he's trying to get his third goal and that just sums him up, he never gives up.
"We're lucky to have him and we need to enjoy him while he's here because if he keeps performances up like this, I hate to say it, but the big guns are going to be sniffing which is what we don't want.
"Luis is the key to that (Champions League qualification). If he can stay in this form and keep producing good performances and goals like that, there's no doubt we'll finish in the top four and that's what Luis wants and that's what he deserves, he deserves to be in the Champions League. A player of that quality has to be in the Champions League.
"I think on current form he's the best player in the world and that's not being biased because he's my team-mate and I'm a big fan of him.
"He scored two today and set up all the others and still hasn't got man of the match and that goes to show how good Jordan Henderson was.
"I'd say it was Brendan Rodgers' best game for Liverpool and I'd say it was Jordan Henderson's as well. Liverpool fans are going away with hundreds of positives from today."