Mourinho is something of an idol to Johnson, 36, and he hopes to pick his brain after their encounter.
"I hope so," he told BBC Sport when asked if he would sit down with Mourinho. "I spent £450 on a bottle of wine!
"I have had to raid my little girl's piggy bank. It is being flown in especially from Portugal."
"It'd be nice to get on as well as I can with him, get chatting to him and trying to pick his brain.
"Jose's right up there - I've read all his books, I've watched any session that's possible to watch, I've studied his interviews.
"He was a player at the same sort of level that I played and hopefully one day I'll be managing at the top level with Bristol City."
The Robins - who have beaten three Premier League sides en route to the last eight - have not played United since a top-flight showdown in 1980, which they lost 4-0.