The last 16 first leg clash at the San Siro brings the charismatic Portuguese face-to-face with United's Alex Ferguson for the first time since he left Chelsea in 2007.
Mourinho has acknowledged he may seem "mad" for wanting to play the Premier League leaders, who had not conceded a league goal in 14 matches before Saturday's 2-1 win over Blackburn.
Inter are nine points clear in Serie A in Mourinho's first season but stumbled through the Champions League group stages.
"I don't want my players to go on the pitch under pressure. I want them to play with pleasure," Mourinho said.
"I've known all about Manchester United since 2004. They're the best team in the world, they play on the counter-attack and we'll have to be very intelligent in how we deal with this."
Dejan Stankovic was rested for the first half of Saturday's 2-1 win at Bologna but is expected to start on Tuesday just behind the powerful front two of Zlatan Ibrahimovic and Adriano.
Three-times European Cup winners United are without defender Nemanja Vidic, who is suspended after being sent off in their Club World Cup final win over Ecuador's LDU in December.
"I just hope I can get two centre backs but at this moment in time it's very doubtful," Ferguson said. "Jonny Evans would have played on Tuesday but he's very doubtful. I'm hoping I'll have John O'Shea fit."
Manchester United: 1-Edwin van der Sar; 21-Rafael, 5-Rio Ferdinand, 22-John O'Shea, 3-Patrice Evra; 7-Cristiano Ronaldo, 16-Michael Carrick, 18-Paul Scholes, 11-Ryan Giggs; 10-Wayne Rooney, 9-Dimitar Berbatov
