Messi is out of contract this summer, and his future remains uncertain following his efforts to try and leave the club last August.
Barcelona won out that time as they kept Messi following a war of words in public, though the Argentine playmaker felt then-president Josep Maria Bartomeu had gone against his word regarding an early termination clause after the season was extended due to the pandemic.
Messi accepted the club's decision, but publicly criticised Bartomeu and Barca - and it seemed like the clock was ticking on the Argentine's time at Camp Nou.
However, Barca are under new management with Laporta back in the presidential hotseat - and he believes that the Camp Nou legend will remain in Catalonia.
Speaking at the presentation of a new documentary titled 'Messi, the tenth art', Laporta said: "Leo Messi's boots will continue on the Camp Nou pitch. He wants to stay.
"I do not contemplate a no. But it isn't easy. We'll do what we can. There is no need to seduce him, he is determined if there are a series of circumstances to stay."
Laporta said a new deal could be announced "... as soon as possible”, but says finding a way around the club’s difficult financial position could be a problem.
"He is OK but he hasn't signed yet. Kun Aguero tells him every day: 'Sign that, we will play together.'
“In economic terms, he has made it very easy, but Financial fair Play is another battleground."
With Barca in a difficult financial position, the club have signed Sergio Aguero and Eric Garcia on free transfers from Manchester City, and are looking to add Memphis Depay on a free from Lyon - but missed out on Gini Wijnaldum, with PSG doubling the ex-Liverpool midfielder's wages.
Keeping Messi is a priority despite those constraints, and Laporta added of FFP: "We have a ratio of 4-1. We have to follow the rules, we will follow them. There will be more sales and loans.
"Without paying a transfer fee. We will do a lot of loans, because we have a very high sports payroll compared to other clubs."