The Red Devils are just a single point behind Chelsea, following their 3-0 win over West Ham on Tuesday.
Vidic told MUTV: “We believe we can win the title. Confidence is a big word, but we believe we can do it.
“They (Chelsea) could be four points in front of us [with their game in hand], but they have to come to our ground [in April].
“We can do it, especially with some big players back from injury. I think we will be good for the rest of the season.”