The European champions travel to Milan this week to tackle Mourinho's men, and they will have to do it without Vidic - who many predict will be Player of the Year in England this season.
Vidic is suspended and Mourinho wants to take advantage, although he still feels that the Serbian should have been suspended for longer after his red card in the World Club championship final in December.
"I think Nemanja Vidic should be suspended for both legs, not just this week's game," Mourinho said in his Daily Telegraph column.
"We will certainly try to make things uncomfortable for the United defence without him at the San Siro.
"We have almost the whole squad fit and with the support of our fans and the experience of our players we can make this very, very tough for United.
"It will not be an open game - we want it to be tight and tactical. So the strikers will not have time and room to work in. That makes it important for us that Zlatan Ibrahimovic produces his very top performance."
Mourinho has already tasted Champions League glory at Porto - although it eluded him at Chelsea, but he is hopeful he can achieve the feat again with the Nerazzurri.
"To win the Champions League with Inter would a great thing," he said.
"This club have not won the trophy since 1965 and that is far too long for a club of this size, with this support.
"Now the challenge is to bring the trophy back to Milan. But first we must defeat the champions."
IbrahimovicAnd Mourinho thinks the key to success will be Ibrahimovic - who he maintains is as good as any player in the world.
"For me he is one of the best players in the world. He has had a very good season with Inter so far and I think we are bringing the best out of a player who needs to have the success to match his talent," he said.
"United have had a great defensive record this season, for sure. But they have not had to deal with Ibrahimovic.
"When players are with me, I always say that my players are the best: this is the way I work. When I was at Porto I always said Deco was the best player in the world.
"When I was at Chelsea I said John Terry was the best central defender in the world, Didier Drogba the best striker and Frank Lampard the best midfield player.
"I don't think Ibrahimovic had reached the right level for his ability before we arrived here. Now, I think he is getting close to what he should be. I think we have improved him a lot. He is scoring more goals, 14 in 24 league games.
"He is more objective driven. His work in the defensive phase has improved incredibly. And the great thing with him is the idea of a player not being able to play every game is completely out.
"He is playing absolutely every game in a fantastic physical condition. I think he's already a very different player and there is more to come."