The Serbian centre-half will see his current deal at Old Trafford expire next summer.
No fresh terms have been agreed as yet, but Vidic has shown over the early weeks of the 2013/14 campaign that he remains an important part of United's plans.
Moyes admits he is yet to discuss the issue with executive vice-chairman Ed Woodward, but sees no reason why the 31-year-old will not be offered the chance to prolong a seven-year stay in England.
He said: "It is something I have not discussed with the chief executive yet but Vida's form at the moment would suggest he is well worthy of that.
"Probably his injuries have been the reason why you might have to look at it, so the big thing is to see how he goes.
"But his form has been very good. We just need to hope he gets through and doesn't pick up any more injuries.
"A lot of attention has been taken by the form of Wayne Rooney and Robin van Persie but defensively, we have done really well and Vida has been excellent.
"I have worked with some really good central defenders. But I have got to say, in the short time I have been here, Vida has been as good as there is."