The former Reds winger has urged the club to sell the wantaway striker because there is no way of guaranteeing his commitment to the side should he remain at Anfield
It has been reported that the striker is preparing to hand in a formal transfer request in order to secure a move to Arsenal, who submitted an improved £42 million bid for the Uruguay international last week.
Barnes has urged the club to sort out the striker's future quickly because he fears it will have no time to find and secure an adequate replacement should he leave.
"We’ve seen in the past when transfers go down to the last minute that it doesn’t help anybody, especially for a club like Liverpool who, if they lose Suarez, would have to find a big-name replacement," he told talkSPORT.
"I’d like it to be done sooner rather than later because if it goes down to the last day, and you then have to go and get somebody, it’s not ideal.
"As far as Suarez is concerned, if he’s not going to be happy, then he has to go. We can all say, ‘yes, we think Suarez is going to be a player like Carlos Tevez, who gives 100 percent no matter what’ but we don’t know what his mental state is going to be if he doesn’t get his wish [to leave the club]."