Le Tissier, who spent his entire career at Southampton, has been highly critical of Cortese's reign at the south coast club.
The Sky Sports pundit was particularly bemused by the decision to sack Nigel Adkins last month despite two successive promotions and signs that the team were beginning to settle in the Premier League.
Cortese brought in former Espanyol manager Mauricio Pochettino despite the Argentine not speaking English and the club have lost one and drawn two games so far under his tenure.
Former England international Le Tissier has been public in his criticism of the chairman and Cortese had arranged to meet him in an attempt to ease tensions.
But Le Tissier wrote on Twitter on Wednesday: "Meeting with our wonderful exec chairman been cancelled #surprisesurprise #somethingtohidenicola."