The Serbian is out of contract at the end of the season, and is yet to agree an extension.
AC Milan were supposedly interested in Vidic during the summer, and could look to sign a pre-contract agreement as early as January if the situation is not resolved soon.
Vidic has enjoyed a glittering career at Old Trafford, which has spanned seven years.
The club captain has won five Premier League titles and the Champions League during his time at Manchester United, and Moyes is desperate for him to stay and add more medals to his collection.
“He is a really top centre half. The best I have worked with, that’s for sure,” he said.
Vidic has returned to playing regular first team football this season after enduring two consecutive injury hit campaigns.
His fitness concerns led to rumours surfacing in the summer that he may well leave Old Trafford, but his performances have impressed Moyes enough to want to offer an extension.
Milan meanwhile are desperate for an experienced centre half who can lead their side, and Vidic fits the bill perfectly.
But David Moyes is willing to fight tooth and nail to keep hold of the former Spartak Moscow man.