That had resulted in talks being arranged between the pair in an attempt to clear the air.
However, Cortese has since opted out of those discussions, having blamed Le Tissier for putting their meeting into the "public domain".
"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," said a Southampton spokesman.
Le Tissier responded by tweeting: "Meeting with our wonderful exec chairman been cancelled #surprisesurprise #somethingtohidenicola."
The Guernsey-born centre-forward spent his entire career with the Saints.