Rumours of a move away from Old Trafford have been rife in recent weeks, but these latest comments have sparked further speculation about his immediate future at Manchester United.
Asked if Shaw has a future at Manchester United, Mourinho said in a press conference: "Why not?"
"He made me feel that I was the best". 'We were one of the best footballing teams in the league...
Manchester United are now preparing to take on Tottenham Hotspur at Old Trafford on Saturday lunchtime.
"Football is full of examples of lack of character and Luke Shaw was just honest". "But we got the player I really wanted".
"I just think l, normally, we have performances at home, normally we trust our game, and yes, the results we can say are positive at home".More news: China has world's 136th most powerful passport, 69 spots behind Taiwan
"So for me they are ideal words that show Luke Shaw's character in relation to the people that he was happy with".
"I think with Southampton he achieved the impossible".
"Eric - let's see, [he will have] one more training session, but he is the only one that I hope from the injured group that can be ready for tomorrow [Saturday]".
"(If) I speak about him I have to speak about Zlatan Ibrahimovic, (Marouane) Fellaini, (Paul) Pogba, (Marcos) Rojo, (Michael) Carrick - so I don't speak".
The two players will be in direct competition for the England left back spot in Russian Federation next summer and it remains to be seen both if this deal materialises and who reaps the greater rewards. But at left back we have so many options, so the situation is not easy. The manager that helped him come to the first team, the manager that helped him to develop in the best moment of his career, is a manager he doesn't forget, a manager he likes a lot, a manager that maybe one day he would like to be reunited again.
Third-placed Tottenham, who thumped Liverpool 4-1 at Wembley last weekend, are level on 20 points with second-placed United after nine games.