Vidic won it with United in 2008 and featured in their two final defeats against Barcelona.
He said: "It would be great to finish by winning it.
"But I believe we can do something special in the Champions League. I really do. If we play solid like we did against Crystal Palace we will be a hard team to beat.
"We always have people who can score goals and that is the way you play in the Champions League - be hard to beat, but be able to score.
"It's the only trophy we can win now, but I think we have done well in the Champions League so far this season.
"Olympiakos is a tough game away from home.
"It is hostile and it is difficult to play there, but if we get a good result we can come back to Old Trafford and finish the game."
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