The Italian businessman wants the Liebherr trust to underwrite his strategy for Southampton to consolidate themselves in the Premier League.
A source close to Cortese, who has overseen Saints rise from League One to the top flight, said he will make a decision on whether to remain as chairman within the next month.
It is understood that Cortese's current frustration centres on those in charge of the trust knowing little about football and not committing themselves to his plans.
Cortese has told the trust he wants to take Southampton to the next level and wants them to support his strategy for doing so, including committing itself to underwriting some modest investment.
Cortese feels he has proved he has handled the club well and his decision, controversial at the time, to replace Nigel Adkins with Argentinian manager Mauricio Pochettino four months ago has paid off with the Saints having all but secured Premier League status for next season.
Cortese was instrumental in the purchase of Southampton in 2009 by Swiss businessman Markus Liebherr, who died suddenly the following year and the club is now owned by the Liebherr trust.