Le Tissier, who was critical of Cortese's decision to sack manager Nigel Adkins and replace him with former Espanyol boss Mauricio Pochettino, had called for a meeting with Cortese.
Le Tissier later revealed that talks had been scheduled for four weeks' time, but Southampton have today told Press Association Sport that those discussions are now off.
"Both parties had agreed that it would be a private meeting with no publicity surrounding it, yet within 24 hours this matter was put in the public domain and further negative comments attributed to Mr Le Tissier have appeared this morning," a club spokesman said.
"As an ex-player, Mr Le Tissier's achievements are well known. However, his repeated criticisms over a prolonged period of time are not justified and have not merited any response from the club. Nor has the motive for these personal attacks ever been made entirely clear.
"For Mr Le Tissier to agree to meet 'in good faith' and then make such comments can only be seen as a breach of good faith and certainly not in the best interests of the club."
He continued: "We would nevertheless encourage Mr Le Tissier to join with our fans and continue to enjoy the success the club has achieved over the last three and a half years.
"The club now considers this matter closed and will not be making any further comment about it."
In October the Saints legend described Cortese as "not a very nice human being", with the Italian later claiming they had never met and Le Tissier told Press Association Sport this afternoon that the meeting's cancellation "doesn't surprise" him and wrote on Twitter: "Meeting with our wonderful exec chairman been cancelled #surprisesurprise #somethingtohidenicola."