Bartomeu, who must stand down in 2021, insisted that he sees Messi "retiring at Barca under another president because he will sign for another spell."
Bartomeu said he spoke to his captain on Saturday.
"I talk to the players very often. Not only with Leo, but also with the group, especially with the captains. Besides, lately we have a lot of topics to talk about," said Bartomeu.
Before beating Villarreal 4-1 on Sunday, Barcelona had drawn three of their previous four matches and slipped four points behind Real in the title race, putting Setien under pressure.
"Setien will continue, of course," said Bartomeu. "I am quite happy with the development we are showing in the games despite the draws.
"I do not regret the change of Valverde. The team needed a boost. Setien knows our DNA, the model and he has brought fresh air and new ideas and is working hard," said Bartomeu before adding that "coaches, evidently, need results."
"If La Liga, which will be difficult, is not won then comes the Champions League in August. We have to try to win one and then the other," said Bartomeu.
He said that Barca are trying to ensure home advantage for the second leg of the Champions League tie against Napoli. The clubs drew the first leg 1-1 in Naples on February 25 before the season was interrupted.
"We are fighting for the second leg of the round of 16 to be played at the Camp Nou. UEFA, if the situation is normal, knows that we would play here," Bartomeu said
In Spain, one of the countries most affected by the pandemic, one of the main outbreaks has been in an inland area of Catalonia, where regional authorities on Saturday announced the isolation of some 200 000 inhabitants in an area around the city of Lerida, about 150 kilometres (93 miles) west of Barcelona.