The Italian businessman is reported to be considering his position with the Saints due to his frustration over the backing that he receives from the trust that owns the club
The Italian has overseen the Saints' rise from League One to the Premier League and wants the Liebherr trust to underwrite his strategy for consolidation in the top flight.
The news prompted manager Mauricio Pochettino to threaten to quit should Cortese leave, in turn prompting the owner to cite such "unity" as a contributory factor in his decision to stay.
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"I would like to thank Katharina [Liebherr, daughter of Markus] for the very helpful manner in which she approached our talks about long-term strategy.
"I am pleased that this matter is now resolved. We can now focus 100 per cent on our preparations for next season.
"We have tremendous momentum now at the club and we are looking forward with great confidence to an exciting and successful campaign next season.
"The last few days have shown me the unity that we now have across the club in the players, the manager, the staff and the chairmanship which normally takes years to achieve.
"I have always believed that to create this unity would make us a very strong club and it is a unity of which I am unashamedly proud."