Messi, 33, is out of contract with Barca in June and is free to sign a pre-contract agreement with another club next month.
Font, one of nine hopefuls running for the presidency, says the immediate priority if he wins the election on Jan. 24 is getting the Argentina forward to extend his 20-year stay at Camp Nou.
"I'm convinced that with a competitive, exciting and, especially in Messi's case, long-term project -- one that could even go beyond the day that Messi retires -- we will convince him to stay," Font told ESPN in an exclusive interview.
"Messi is the best player in the history of the No. 1 sport in the world. Imagine what that means. For that reason, the Messi-Barca association is a strategic one and we must do everything possible to guarantee the association lives on.
"Keeping in mind he can speak with other clubs in January, phoning Messi [if I win the election] must be one of the priorities."
Font, who has not spoken with Messi's people yet, has been working on his candidacy for several years and says he will find a place at the club for former midfielder Xavi, currently the coach of Al-Sadd in Qatar, if he's elected.
"[Xavi] is one of the most important parts of the sporting project we have designed," he added.
"The fact Messi and Xavi know each other [is good]. Xavi is someone Messi trusts. I know Messi would welcome the leadership Xavi can bring.
"But it's about the whole project, not just one person. What's important in the Messi case, to excite supporters again and, above all, to emerge from the complicated situation the club is in at all levels, is the whole project. It's not one name or a coach, it's the whole structure."
Barca have been hit harder than most European clubs by the coronavirus pandemic. Revenue last season was down €231m on what they had budgeted for and debt rose to nearly €500m.
Font is aware the club is "on the verge of bankruptcy" and acknowledges, therefore, it will be difficult to offer Messi a deal worth as much as the €100m he roughly earns annually at the moment.
"Messi, above all else, is a person that loves Barca and what he wants is to win," he said.
"Of course, the best player in the world and the best of all time has to be compensated competitively. But I think his priorities are competing and winning.
"[His salary] is one of the realities that has to be adjusted. The level of revenue in the short-term and for next season is up in the air. It depends on what happens with fans coming back to the stadium.
"Based on that, we will have to structure the wage bill appropriately. Once we are clear on that situation; we will know what the club can afford.
"Messi is a Barca fan and he loves Barca as we all do. He's been here for a lot of years, since he was 13, and I am sure that regardless of what he wants to do [with his career] to keep winning, his passion and love for the club is more than anything else."