Suarez signed a new contract extension at Anfield last week giving him a bumper pay rise and keeping his tied to Liverpool until 2018.
The Uruguayan has been in stunning form this season and the Reds were vindicated for rejected a whopping bid of more than £40million in the summer from Arsenal.
The 26 year old is a reported target of Real Madrid too and Barnes believes that if Liverpool fail to qualify for the Champions League once again this season, Suarez may still be off this summer.
“Liverpool need to finish in the top four to have any chance of holding on to Suarez,” Barnes said.
“That’s not to say though that, by qualifying for the Champions League, he will definitely stay.
“He’s signed a new contract but, even if they finish fourth, if Real Madrid come in [then he’ll leave]
“I would love him to stay but I can’t say hand on heart that he will in the summer.”