The future of Saints has been uncertain since former owner Markus Liebherr, who saved the club from going bust in July 2009, died in August with reports suggesting the Swiss businessman's family were looking to sell up.
But Cortese told BBC Sport: "The club is not for sale. 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.
"If there's any lack of commitment 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%."