Messi struck a hat-trick in victory over Granada.
"It's unlikely that another player like Leo will play [this sport] and break this record," said Bartomeu.
"We have a fantastic player for many years to come. We're privileged."
On Pep Guardiola's contract situation, Bartomeu added: "He's an important person, he turned this team around, the Club and Barça's athletic vision. We want him to stay. He represents much more than a manager and we hope that he stays."