Messi re-signed with Barca in 2017 – an extension that runs through to 2021 – and the five-time Ballon d'Or winner has not slowed down this season.
The 31-year-old, who made his competitive debut for Barca in October 2004 at the tender age of 17, has scored a LaLiga-high 32 goals in 2018-19 and 42 in all competitions.
Bartomeu wants to renew Messi's contract at Camp Nou, where he is Barca's all-time leading goalscorer.
"We want him to have a really long career so we can keep on enjoying him," Bartomeu told ESPN . "Lionel's managed to break down borders. Everyone admires him and he's applauded at other stadiums by rival fans.
"We would like to renew his contract, that's the idea. He is young – you can see that [in his performances] – and he still has two years on his deal. He's always improving, always innovating. I believe he still has many years in front of him and in the coming months we will sit down with him so that he has many more years at Barcelona.
"Messi is a one-club man. It's more than what he does on the pitch – his relationship with Barca will last forever. I use the example of Pele, who was always at Santos. We want Messi to always be at Barca, whether that's playing or linked to the club [when he's retired]."
Messi came off the bench to rescue an incredible 4-4 draw at Villarreal on Tuesday as La Liga leaders Barca kept their treble hopes alive.
Bartomeu added: "Messi changed completely the sense of Barca. In the way of keeping our club on top [in terms of] results, [winning the] top competitions and trying to win every season.
"Messi knows his body well and the day he believes he can't add [what he wants], he will leave. [We have] to prepare for the future. Leo Messi is our leader, he's the best player in the world of football, he's playing with us, he's playing fantastically, but we know it won't be forever.
"Maybe in three, four or five years, Leo Messi will say: 'OK, I am going to stop playing football.' So we are preparing our club for the future, for the time post-Leo. Because we would like to still be the top club at that time. So, it's a way of working, of investing, also of taking risks.
"We invest in young players, on homegrown players from La Masia, but also on bringing players from other clubs, just to keep this level of excellence."