The two sides enjoyed entertaining games in the Championship last season – United winning 4-1 at home, before drawing 3-3 away – and will resume hostilities in the top-flight after Villa beat Derby in the play-off final in May.
United and Villa are both managed by supporters of the club, while club captains Jack Grealish and Billy Sharp also support Villa and the Blades respectively.
And Wilder said: “The run Dean went on when he took charge of Villa was brilliant… club records broken here, there and everywhere.
“I know Dean well and the work he did at Brentford and going into Aston Villa.
“Everyone talks about boyhood fans but he would have been under huge pressure, and put huge pressure on himself, to get results and the manner in which he did it was outstanding.
“The final was a tight game and I was delighted for Dean and his players.”
Villa subsequently spent multi-millions on new players in the summer, while United lavished around £40m on signings – a modest amount by Premier League standards.
“It’s up to the clubs how they go with finances,” Wilder added. “Every club is different. We did what we did and Dean did what he had to do.
“I’m looking at it as a great game.”