Lampard enjoyed the best years of his playing career under Mourinho at Chelsea, and the pair will battle it out in the dugout on Tuesday night when the Rams travel to Old Trafford.
The Blues legend has revealed that the pair have already spoken ahead of the contest, but opted against extensive discussions about the match in the North-West.
At a press conference, Lampard told reporters: "I'm looking forward to seeing him. On a personal level, he was a manager who was very influential on my career.
"We've spoken in the last 24 hours to congratulate me but it was very brief but we talked family. I learned a lot from him and I appreciate it."
Lampard has guided Derby to seven wins and a draw from his 11 matches in charge of the East Midlands outfit.