Tusquets met with the three candidates for the presidency -- Font, Joan Laporta and Toni Freixa -- earlier this month and it was agreed that, due to the club's financial situation, they would wait until the summer to sign Garcia, when his contract expires with City.
However, Font has made a late attempt to get the club to change their mind and push through a signing that coach Ronald Koeman has requested.
"We're asking the acting board to sign Eric Garcia," he said in a news conference on Wednesday. "Koeman's asked for him, our sporting structure [if we're elected] support it and the player wants to come because there's a European Championships this summer.
"He [would be] fundamental in the fight for three trophies this season. We know City would accept €3m plus add-ons and we wouldn't have to pay until next season -- that's a lot less than Barça offered four months ago.
"The player's also ready to make a big effort and not be paid a salary until the end of the season."
Barca failed to reach an agreement with the Premier League side in the summer but the player remained hopeful of making the move this January.
But while he has Font's support, a move this week before the window shuts remains unlikely if fellow candidates Laporta and Freixa don't get on board.
Laporta has said that, due to the club's rising debt, it would be irresponsible to commit money to a signing this month when he's available for free this summer.
Barca's accounts, dated August 2020, surfaced this week and revealed that the club's gross debt has risen above €1 billion. Font concedes that the club, therefore, will be limited in the transfer market in the immediate future and called for further wage cuts.
"In the coming months we can't make big investments in signings," he added. "We're combing the market for players that are out of contract this summer and whose salary is compatible with the club's situation.
"We have to restructure the wage bill and lower it. We must be honest. We have to decide which players are indispensable."
"Haaland would be one of the best signings Barca could make," he said. "If the sporting structure considers him a target, it would be very interesting, although we understand it won't be possible in the next 12 months."
Barcelona announced on Tuesday the election for a new president will take place on March 7, over four months after Josep Maria Bartomeu resigned from the position.