The deposed German champions clash with Los Blancos in the Champions League semifinals later this month and the Real Madrid boss went to see his side's opponents in action on Saturday. BVB triumphed 6-1 at the Trolli Arena and Klopp feels Mourinho's exit when Dortmund was 5-0 up means he did not see anything useful.
"We are no longer in the situation where we want to play well for Mourinho. He will have got some impression, which he cannot use in two weeks, because everything will be different," Klopp told Sky. "But if he wants to see Furth, he is welcome ...
"He left after the 5-0 and didn't see our weaknesses. But if he wanted to see whether [Mario] Gotze can play on the left, he can call me."
Gotze and Ilkay Gundogan netted two goals apiece, with Jakub Blaszczykowski and Robert Lewandowski also getting their names on the scoresheet in the lopsided win.
BVB hosts Madrid on April 24 before travelling to Estadio Santiago Bernabeu for the return leg six days later.