Warnock was sacked after Saturday's 1-1 draw away at promotion hopefuls West Brom.
The Englishman's new team sit 14th in the second tier, but are just four points off the play-off places.
Wilder guided Oxford out of the Conference in 2010 and won League Two with Northampton in 2016.
Former manager Warnock believes Wilder will be 'given what he wants' to get the right players in for a promotion push.
The 1,063-game vet said after Saturday's draw: "I'm disappointed how it's ended up but nothing surprises me really. I found out this morning, with a call to say they were going in a different direction.
"I felt I deserved a bit more but it's not to be and I wish them all the best because it's a great club with super players.
"Whoever comes in will get a great set of lads and will get some support in the transfer window. I think the new man will be given what he wants to get three or four players in.
"They need those players and, then, I think they still have a good chance of going up. I will look from afar and see how well they do.
"I'm proud of my managerial record and I can't see it being beaten in the modern day. I've had a really good time."
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