Suarez joined the club in 2011 and has since gone on to score an impressive 73 goals in 155 games for Liverpool.
But Barnes likened the striker to ex-Liverpool player Fernando Torres, whom he thought could go on to achieve legendary status but instead left the club too soon.
"He is a fantastic player and we would like to see him stay there for a long period of time," Barnes told Sky Sports.
"When we talk about legendary status he has the ability to do it but then Torres showed it for the first two years and he's not there anymore.
"You have to be there for a particular amount of time to be considered a legend for any club, but I would love to see him stay and do it."
Barnes, who had a 10-year span at the club, says the most impressive aspect about Liverpool this season has been their consistency with or without the presence of Suarez.
And he admitted that he would be disappointed if the Reds failed to finish in the top four this season.
"More pleasing for me is that even when he has not played the team still looks competent, Barnes said.
"We are not just relying on him, we are playing in a way that suits the players which means that they can play consistently well and create chances.
"Jordan Henderson for me has been a revelation so the future looks good for Liverpool.
"But I would be despondent if all of a sudden they did not finish in the top four."
@F365 - Barnsey says "I won't be despondent..." not "I would be despondent...". Big difference.- CaptainRaj