After the 44-year-old Italian business magnate denied having ever met the former England international before during an interview with Sky Sports last month, Le Tissier urged a personal meeting between the pair so that Cortese could clarify his comments, which he claims are false.
This is the latest step in what has quickly become an increasingly public feud, with Cortese previously stating that his door was always remain open to those who have the best interests of the club at heart and Le Tissier has taken him up on his offer, even if he disagrees with his version of events.
"I got a call Friday, after I rang them on Monday, saying that he is quite happy to have a meeting with me in good faith," Le Tissier told reporters.
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"He said he could could make it in four weeks’ time, and it would more than likely be in London.
"He flat out lied in that interview. He said he’d never met me, which was a complete lie, considering I was in the boardroom speaking to him for about 15 minutes before the first game that they [late owner Markus Liebherr and Cortese] were in charge, against Millwall.
"That was why I decided to ring up the football club and ask him for a meeting, because I believe I come into that category.
"You should be together as one and you shouldn’t alienate people as he has done."
When asked what he hoped to gain from the face-to-face meeting, Le Tissier admitted that he wanted to address the interview in question while also discussing the topic of the reported banning of his former team-mate and club stalwart Francis Benali from St Mary's Stadium.
He added: "I would like to ask him some questions about what he said in his interview, and about what he’s done to some of my friends.
"I would like him to look me in the eye and give me some reasons why he’s done the stuff he’s done.
"If he doesn’t think Franny Benali has got the best interests of Southampton Football Club at heart he’s very much mistaken.
"Southampton Football Club means more to Francis Benali than it ever will to him, and for Franny to be banned from the football club is, in my opinion, nothing short of disgusting.
"His actions are very different from the words that he spoke in that interview, and I’d like to question him on it."