The Uruguay international has expressed his desire to extend his stay at Anfield despite a testing first full season and Carragher believes it is "vitally important" to keep hold of the 25-year-old.
Suarez scored Liverpool's all-important equaliser in Saturday's FA Cup semi-final victory over Everton - his 14th goal of the campaign - in an improved second-half performance.
And while his finishing has not been as prolific as he may have liked Suarez is still the club's leading scorer this season and his threat to defences has remained undiminished.
"I thought he was brilliant. Our best player. I wouldn't swap him for anyone in the league," said Carragher.
"He is a fantastic player and I'm delighted we've got him and hopefully he will take that forward into the cup final.
"It is vitally important (Liverpool keep Suarez). I see no reason why he would want to leave.
"He is playing well so hopefully he will sign a new contract, which he is expecting to do."
Suarez had been linked with a move to newly-rich Paris St Germain as speculation began to grow about his long-term future in England.
Those were prompted by presumptions about his unhappiness at the eight-match ban he received after being found guilty of racially abusing Manchester United defender Patrice Evra last October.
The Uruguayan, however, has dismissed suggestions he wants to leave Anfield just 15 months after arriving from Ajax in a £22.8million deal.
"I will continue at Liverpool. It is obvious I will continue," he said.
"I have four years left on my contract and I am very happy and content to be here and I hope to do great things."
As if to underline that he stressed he had put the Evra incident firmly behind him, although he did hint it may have affected his form.
"I am over that. Obviously the important thing was the support from all the people and there is no need to talk about that as it is already in the past," he added.
"I have to thank the people of Liverpool for the support they have given me despite not playing at my best.
"I am accustomed to it (criticism), one just has to deal with it and face up to it."
After the weekend's Wembley win captain Steven Gerrard was keen to give his backing to Suarez's partnership up front with Andy Carroll, who has been much less of a success since his £35million move from Newcastle at the same time the Uruguayan arrived.
And after scoring the late winning goal - for the second match in succession - his team-mates were queuing up to give their backing to the big striker.
"You have to do your best every time otherwise you will get criticism," said defender Daniel Agger.
"It is normal in football when you don't play regularly.
"I think he has shown he has got potential and to score a winner that late is always a great feeling."
Liverpool will meet Chelsea twice in four days next month after their Barclays Premier League clash at Anfield was rearranged to May 8.
The fixture, the Reds' last home game of the season, was originally due to be played on May 5 but the two clubs will meet in the FA Cup final on that date.
It means the pair will have played each other four times this season, with Liverpool having knocked Chelsea out of the Carling Cup in November.
The Merseysiders have won their last four encounters against their Stamford Bridge opponents.