Messi, who failed to turn up for pre-season training on Monday, had previously labelled his side 'weak' and 'inconsistent' after surrendering the league title to rivals Real Madrid.
According to widespread Spanish media reports, Netherlands coach and former Barca defender Ronald Koeman is set to be named as Setien's successor.
Calling his side 'weak', 'inconsistent' and 'very easy to score against', Lionel Messi called for urgent changes
But Font believes Messi's love for Barcelona, who he joined aged 13, is so deep that he could lower his salary demands in order to stay.
Barcelona pulled off a stirring comeback to overturn a two-goal deficit and reach the Copa del Rey final, beating Sevilla 3-0 after extra-time in Wednesday's semi-final second leg, to go through 3-2 on aggregate.
News of all that's transpired on and off the football field.
News that transpired on and off the football field.