The left-back played under current Spurs manager Mauricio Pochettino at Southampton, where he came through the ranks before making a £30m switch to Old Trafford in 2014.
The manager has publicly criticised the England international numerous times and he did the same again following the Red Devils' FA Cup quarter-final win over Brighton, in which Shaw was substituted at half time.
While giving his take on the situation, Le Tissier told Sky Sports News: "I think if Mourinho is still there then it is inevitable Shaw will leave this summer. I have no idea what he is trying to achieve.
"There is just a really strange relationship going on there and I don't understand what he's doing because he's just destroying the player at the moment.
"I'm not sure if it was anything to do with him choosing Manchester United over Chelsea despite being a Chelsea fan when Mourinho was manager at the time.
"You also don't know what happens at training or how he lives his life to give an accurate assessment but, while there are players that this sort of approach can work with, I just don't think Shaw is one of them."
When asked about Shaw's future, Le Tissier suggested that the 22-year-old could move to Tottenham, with Danny Rose heading to Old Trafford.
"Having worked with Pochettino before and spoken highly of him, it would seem obvious for him to go to Tottenham with Danny Rose potentially going the opposite way as he is obviously desperate to get back up North," he said.
Shaw has started 12 games in all competitions for United this season.