The pair are famously at odds with each other, but are now due to hold talks in about four weeks’ time.
Le Tissier called for a meeting after hearing comments made about him by Cortese in a recent interview on Sky Sports News.
He contacted Saints just over a week ago with a view to arranging talks, and subsequently received a response via the club secretary, Ros Wheeler.
“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," said Le Tissier, who added that Cortese wishes for only the two of them to be present.
“He said he could could make it in four weeks’ time, and it would more than likely be in London."
In his interview on Sky, which was conducted by presenter Jim White during the club’s trip to Barcelona last month, Cortese was asked about his relationship and supposed “feud” with Le Tissier.
The St Mary’s chief said: “You just mentioned this individual. I don’t even know him. He has never met me. I don’t know what his issue he seems to be having with me (is).
“I think any one of the people involved in the past or associated to the club who has been stirring negativity towards me they should probably ask themselves as well whether this is beneficial for the club.
“You never hear me saying anything badly about them. Also, again, because I would not allow myself to characterise or to judge a person I have never met.”
Le Tissier has taken exception to Cortese’s claim that they have never met.
“He flat out lied in that interview,” said Le Tissier. “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 (league) game that they [late owner Markus Liebherr and Cortese] were in charge, against Millwall.”
The man voted by fans as the greatest player in the club’s history said he was also prompted to approach Saints after hearing Cortese’s assertion that “Everybody – I’m not excluding anyone – who has got Southampton at heart has got a place at our club.”
Le Tissier said: “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.”
Asked what he hopes to achieve from the meeting, Le Tissier said: “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.”
Le Tissier particularly wants to address the issue of the treatment of his close friend and former teammate, Francis Benali, who he says is banned from the club.
“If he doesn’t think Franny Benali has got the best interests of Southampton Football Club at heart he’s very much mistaken,” said Le Tissier.
“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.”
Le Tissier added: “His actions are very different from the words that he spoke in that interview, and I’d like to question him on it.”
Le Tissier said he also wants to broach the subject of Cortese’s relationship with the Ex-Saints Association, which is understood to have soured.
Despite their clear differences, Le Tissier believes it is possible for he and Cortese to find a way to move forward.
He said: “We’ll probably never be best of mates, but if he starts treating people with a bit of respect, and I’m not talking about myself – he can treat me how he wants, it’s not going to change the way I feel about the football club – but there are a lot of people that have been affected by some of the stuff he’s done, and I don’t think it’s right.
“If he wants to right those wrongs and start with a clean slate so be it, and as he says ‘move together as one’.”
The Daily Echo contacted the club to offer them the opportunity to respond to, or clarify, any of the points made, but did not receive a response by the time of going to press.