The Portuguese worked with the striker at Inter and expects him to be fired up to win the Champions League against his side in the quarter-finals
The 32-year-old played under the Portuguese at Inter, but joined Barcelona ahead of the 2009-10 season – the same year in which Mourinho led the Nerazzurri to European glory.
Despite being on course to collect an 11th career league title with PSG this season (including the Serie A medals that were revoked due to the Calciopoli scandal), the Sweden international has yet to prevail in the Champions League.
And Mourinho, whose Chelsea side face the French giants in the last eight of the tournament, expects Ibrahimovic to be extra-motivated to at last claim silverware in Europe's premier club competition.
"But Zlatan is a special player, who has won all the championships and he wants to win the Champions League now. It is a dream for him and he will do anything to accomplish it, which will make him even more dangerous."
Mourinho is not taking the threat of PSG lightly and argues that the capital club's healthy 10-point lead at the top of Ligue 1 gives them an advantage, with Chelsea locked in a three-way battle for the Premier League title that looks set to go down to the wire.
"Paris is a team with very good players. Paris is already a champion and this is an important advantage," he added. "They already think about Chelsea and not Nice [on Friday].
"For us, it is different in the Premier League. All matches are a final for us. Against Crystal Palace [on Saturday] it will be a final.
"Paris is the favorite thanks to this small advantage. They have no experience in the Champions League but have quality players. They have an outstanding attack and this is very important.
"But the history of Chelsea in the Champions League can help us. We are not under pressure. This scenario does not bother me, it suits me. I do not want to be misinterpreted and people say I'm arrogant. It will be 50-50."