Reports in recent weeks have suggested that the League One club could be sold by the family of Swiss billionaire Markus Liebherr, who died in August.
Cortese told BBC: “The club is not for sale. There’s always been a group behind the scenes with an agenda that’s not good.”
Cortese, who conducted the deal to buy the club in 2009, added: “The commitment even after Markus passed away is exactly the same, and nothing has changed.
“This is a deliberate attempt to damage the club at this time because we’re in negotiations with players and a very important [potential sponsorship] brand.”
“Southampton are in a very strong position and people envy that fact,” he continued.
“If there’s any lack of commitment [from the family] we have a plan B. I know people with money who would have the same attitude as Markus who would join us on this. But, just to underline, the commitment of the family is 100%.”
“I have been the boss of this from the beginning,” he said. “Markus never made decisions, I did, and that is the same now.
“A few weeks after he died I was struggling with motivation, but it’s not just about Markus now, it’s for the people of Southampton and the legacy of Markus, I owe it to him. I’m driving his vision on.”