The Cypriot champions have been the surprise packages of competition, winning five of seven home games on the way to becoming the first team from their country to reach the last 16 of Europe's premier club competition.
"They eliminated top-class teams. We have studied them a lot," Mourinho told a news conference at the GSP stadium.
"We are the favourites, but football is football. I am sure that we are not going to have teams certain for the last four from the first leg," he said.
"Of course, having the second leg at home makes things more easy for us," added the Portuguese who has led the nine-times European champions to the top of La Liga this season.
APOEL's success has been based on a dogged defence and they will be roared on by their passionate fans.
"It is a very difficult match and we must give a top performance against one of the best teams in the world," said APOEL coach Ivan Jovanovic.
"I achieved almost everything in the last four years with APOEL, but I still have a dream. To eliminate Real," said Jovanovic whose side knocked out Olympique Lyon on penalties to reach the last eight.
Asked about that comment, Mourinho replied: "Coaches are allowed to dream when their players allow them to, and since they are at this stage of the competition they are allowed to dream.
"APOEL is a very balanced team. For many, this may mean nothing, but for me it means a lot and I hope my players realise this too," Mourinho said.
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