Lage was axed by Benfica after last night's Champions League defeat to Qarabag.
Benfica president Rui Costa has stated he expects the new coach to be installed before the weekend.
And Lage admits he expects Mourinho, who is free after being dumped by Fenerbahce last week, to replace him.
"The most important thing is to wish Benfica all the best," he said, reported by A Bola. "We've worked hard since the start of the season with a radically revamped squad, but unfortunately, certain internal and external constraints have prevented us from moving forward.
"I wish the next coach good luck. I don't know if it will be Mourinho or someone else, but he will certainly be someone who knows Benfica well.
"With the arrival of players like Sudakov and Dodi Lukebakio, he will have even more tools to do well."
Lage concluded: "The players have always followed my instructions, I feel fulfilled. I love Benfica; they have done so much for me and my career, pushing me beyond all expectations and giving me the means to support my family."