The former Germany midfielder has spoken to the coach recently, with the Portuguese revealing his admiration for the dethroned Bundesliga champions
The two sides faced one another in the group stages of the competition, with BVB taking four points off the reigning Liga champions, following a 2-1 win at Signal Iduna Park and 2-2 draw away at the Santiago Bernabeu.
Since then both sides have been cut adrift in their respective leagues, with Dortmund dethroned as champions by Bayern Munich and Madrid set to surrender their crown to Barcelona, despite an improved run of form in the second half the season.
And with the two clubs set to do battle again on the back of Friday's Champions League draw in Switzerland, Effenberg revealed Mourinho's admiration for his European opponents.
"I spoke to Mourinho a few weeks back," the former Germany midfielder told Sky Sports News.
"He told me that he has great respect for Dortmund. Dortmund have nothing to lose and if have already achieved an awful lot. If they beat Real that would be absolutely sensational.
"Dortmund are the underdog for the tie, but they have surprised us all. Real are much stronger than in the group stages, but Dortmund are capable of beating them."
Bayern Munich were paired with Barcelona in the other semi-final tie and after suggestions FCB could call upon coach-to-be and former Blaugrana boss Pep Guardiola for advice, Effenberg has moved to dismiss that notion.
He added: "There will be no call to Pep. Jupp Heynckes is experienced enough to know what to do.
"Barca have a small advantage, but Bayern Munich are incredibly strong. It is important Bayern do not hide and they cannot focus all their attentions on Messi - you cannot completely turn off a player like Messi."