The Argentina international extended his stay with the club last year until 2018 and is reportedly on the verge of agreeing a new deal.
Bartomeu expects Messi to put pen to paper and also believes he will remain at Camp Nou for the foreseeable future.
"Messi will continue at Barca. His current contract will not be his last. He will sign more," Bartomeu told COPE.
"I think I'll leave the club before Messi does.
"Everyone wants to re-sign Messi to Barcelona. He's a unique player, the best in the world and we're enjoying him.
"There is no problem renewing. We want him to be the highest-paid player in the world."
Messi highlighted his importance to Barca yet again with an El Clasico hat-trick against Real Madrid on Sunday before scoring again in Wednesday's 3-0 victory over Celta Vigo.
Those back-to-back wins keep Gerardo Martino's men firmly in the Liga title running after what has been a below-par season by the club's own recent high standards.
Bartomeu is happy with the progress being made and expects Martino to see out his contract.
"Tata has a contract and he has said he will comply with it. It's true there is a clause that can terminate it but we are very happy with Martino," he added.
"The expectation is that he will comply with his contract."
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