World Cup-winner Khedira has denied reports he refused to sign a termination agreement with the Serie A champions, but he is set to leave and England's top flight is his desired destination.
"When I was a child, it was always a big dream of mine to be a Premier League player," the 33-year-old, whose contract expires at the end of the season, told Sky Germany.
"I am really happy and satisfied with my career until now but one thing is still missing because I always had this dream and it has never come true… to be a part of the Premier League.
"I have watched so many Premier League games since I was young; even now I am following the Premier League a lot.
"I enjoyed always to play with my teams to play in the Champions League against the English clubs. The atmosphere, the style and idea of football has always impressed me.
"If it is possible, it will for sure be a really big dream [come true] and honor to be a part of the Premier League."
Explaining his respect for the Portuguese, Khedira said: "Because of his personality, he is always honest, direct, clear in his mind and a great coach.
"Many people talk about him [being] too defensive, but he is a winner, he is a champion. That is why he impressed me the most."
But Mourinho is not the only coach in the Premier League who has won the admiration of Khedira, with Everton manager Carlo Ancelotti also coming in for praise.
"I really enjoyed working with Jose Mourinho but there are many coaches who I would like to work with," said Khedira.
"I would never say no again to Jose Mourinho but it is not the only guy who I would say I would like to work with again.
"There are many coaches, even in the Premier League that I respect a lot. Ancelotti is doing a great job at the moment and is a great personality.
"He is one of the coaches who impressed me also."