Koeman was on Tuesday, officially unveiled as Barca’s new boss, following Quique Setien’s sack.
Current president, Josep Maria Bartomeu, is under increasing pressure with elections set to hold on the first match day of March 15, 2021.
Font is in the running to replace Bartomeu, who has been in the role since 2014.
And speaking on Spanish radio programme El Larguero on Tuesday night, Font said: “Even if Koeman has a great season, I will not change my plans.
“If I become president, Koeman will not be the coach of Barca in the 2021-22 season.
“Xavi understands that all the puzzles in the club must be put together. Who will lead the team will be decided by the Board of Directors, in our case it will be him [Xavi].
“Messi is completely disappointed because of the critical situation at the club both in sports, and in economic and organisational terms. I expect that Messi will play under Xavi in 2021.”
Xavi is managing Al-Sadd in Qatar.