There has been much talk this week about the future of the Italian businessman, who was instrumental in the club's purchase by Markus Liebherr in 2009.
Cortese stayed on after the Swiss billionaire died suddenly the following year and helped the club rise from League One to the Premier League.
Saints head into Sunday's final game against Stoke with another season in the top flight already assured, although whether Cortese is there to see it is another matter.
Press Association Sport understands he is considering his position at the club due to frustrations over the backing he receives, feeling those in charge of the Liebherr trust are not committing themselves to his ambitious plans.
The executive chairman will make a decision on whether to remain at the club within the next month and manager Pochettino confirmed on Thursday if Cortese leaves, so will he.
"I am a very honest person and I am very, very grateful to the people that put their faith in me," the Argentinian, who controversially replaced Nigel Adkins in January, said.
"I would not understand staying in this role if Nicola was not here.
"The person that actually called me from the start, told me about the project and put their faith in me was Nicola.
"I have great respect as well for Southampton, the club and the supporters, but Nicola has been the one that has placed his trust and faith in me.
"I wouldn't see myself in this club if it was not for him.
"I think I am a very transparent person, a very honest person.
"We are on the same wavelength about the club and the future of the club so it really would not make any sense if I was at this club and he was not.
"We have a clear path of how we want to proceed in the future, how we want to place Southampton as high as possible in the table, so we are very clear on those goals, those ideas on how to do those things so that is how we want to proceed.
"We are united in the passion we have for this club, the project we have for this club so we are fully committed and fully united in that idea."
The former Espanyol manager's forthright comments at this morning's press conference came as a surprise to many, especially as he does not expect to have to go through with his threat.
Pochettino spent much of the time speaking about a bright future and how he hopes to do most, if not all, of his transfer business by the start of July.
The former defender is having a series of meetings about next season from this afternoon onwards and revealed he will not be returning to his native Argentina this summer in order to focus on the new season.
Instead, he will split his time between Southampton and his adopted home of Barcelona in the belief that Cortese will receive the assurances he requires.
"I have total confidence, total faith that Nicola is going to be here for next season," Pochettino said.
"We are all working towards that goal, towards next season to have everything prepared by July 1 so I have total faith that I will be here and Nicola will be here for next season.
"We are going to have a few meetings this afternoon and throughout next week as well, but I haven't heard anything else.
"We are all working as if everything is continuing as normal. We're all working for the future of this club for next season, the preparations for next season.
"We want to have everything tied down and set up by July 1 so we are all continuing working as if everything is staying as it is."