The Premier League giants reached the last eight on Tuesday after completing a 3-1 aggregate victory over Galatasaray with a 2-0 win at Stamford Bridge.
A potential meeting with Olympiacos, who lead Manchester United 2-0 after the first leg, shapes as arguably the most favourable draw.
Mourinho said facing one of the favourites – Bayern Munich, Real Madrid or Paris Saint-Germain – would be welcomed by his team.
"All the big teams are there, all the big candidates to win the competition are there. We welcome any of them," he said.
"It will be very important for the evolution of our team to play one of the best, so we wait for the draw."
First-half goals from Samuel Eto'o and Gary Cahill saw Chelsea to a relatively comfortable second-leg win.
Mourinho was pleased with the way his side controlled the clash, with Galatasaray having few chances.
"It was a very good performance. We were very solid, very compact, and had no fears – a very good approach to the game," he said.
"(1-1) is a difficult score but our game was very solid. We were very confident and very much in control for the entire 90 minutes, which is difficult.
"We got a positive result in the first leg and in the second leg we finished the job."
Didier Drogba's return to Stamford Bridge was a disappointing one as the Ivory Coast international got few chances.
Mourinho praised Cahill and John Terry but said Drogba was left isolated and could do little to help Gala avoid defeat.
"The most difficult thing (for Drogba) was the way his team played because if you are striker and the team is not there playing behind you then you are a lonely man," he said.
"It has happened to every striker in the world and tonight it happened to Didier. Gary and John played a very good game.
"We controlled the match very well and you could never see Didier in a dangerous position."
