Mourinho was appointed as Spurs head coach on Thursday after the departure of Mauricio Pochettino, who led the club to a UEFA Champions League final last season.
Klopp is delighted to see Mourinho return to the top flight England but is sad to see Pochettino leave just five months after their meeting in the UEFA Champions League final.
"Welcome back, Jose! Obviously it's nice to have him back. He was desperate [to come back], you could see in the time when he was not in.
"But on the other side, Mauricio is not there anymore and that shows how quick things change nowadays.
"About five months ago we played each other in the Champions League final and now he is on holiday. I hope he can enjoy it, to be honest.
"He did a brilliant job at Tottenham, nobody doubts that, everybody knows that. He's an outstanding coach, a great guy.
" I really enjoyed the games we played against each other; my first game in the Premier League was against him so we have a history together.
"Pretty much all the jobs that are available or not available, Mauricio will be in contention I think.
"Everything will be fine but of course that was a big one - when I heard it first I couldn't really believe it in the moment, but a couple of hours later they had a solution.
"I really hope that Mauricio can enjoy the few days, weeks, months off, it will not last long. Then he will be back.
"Jose is highest motivated obviously, so that will be interesting as well."