The star forward struck with an incredible free-kick to bring up 600 goals at Barcelona, the club he joined at 13.
While Bartomeu feels Messi will remain at Barca for several more years, he said they were slowly planning for the future.
"He might even play until he's 45, who knows? We know he'll play three, four, five years more, we don't know how many – as many as he wants," he said, via The Guardian.
"We're preparing. Players like [Ousmane] Dembele, [Clement] Lenglet, Arthur are there to build a team for when Messi stops playing, but I still see it as a long way off. I don't think that day is near. And we tell the players who play and train with him: 'Make the most of every minute'.
"We are talking to the family but it's very early to say. He's a footballer. So we talk football, but he will stay here with us. He's a club man.
"I talk always about Pele, who was always associated with Santos, the only place he played. Leo belongs to world football, but he has always lived at Barca. He will be a one-club man. Leo will never leave. He'll stop playing, but he'll always be with us."
Messi is a five-time Ballon d'Or winner among numerous other honours, having helped Barca claim 10 LaLiga titles and four Champions Leagues.
Bartomeu said that while Messi was incredible, he had made his feats seem normal.
"Leo is a genius and it's been so, so many seasons, so, so many games," he said. "We live an extraordinary era but for our fans, it feels normal."