Klopp's men are in the decider of Europe's premier club competition for the second straight season, facing Tottenham in Madrid on June 1.
Mourinho, a two-time winner of the Champions League, said another loss for Klopp would hurt.
"If Jurgen wins it's an incredible achievement for him," Mourinho told Sky Sports.
"If Jurgen doesn't win, you know... to lose three Champions League finals... phew... that has to be really, really hard, but he is a very positive guy, I'm sure he's just thinking about winning.
"Being a manager, and understanding what it means for a manager to play a Champions League final, there is always a negative side of it and the negative side is that one team will lose and one manager will lose."
Tottenham manager Mauricio Pochettino is also yet to win a trophy at the helm of Spurs, although he has achieved top-four Premier League finishes in the past four seasons.
Mourinho believes a win at the Wanda Metropolitano could lead to a period of sustained success for Tottenham.
"Spurs are not winning titles and to win the first one would be fantastic and could lead to other domestic trophies because the Champions League is the biggest one of all," he said.
"Finals are not to play, finals are to win."