Barnes, who played for Liverpool between 1987 and 1997, believes a deal to sell the 26-year-old should be completed as soon as possible.
Speaking on talkSPORT, he said: "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.
"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 per cent 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 Liverpool)."