United opened talks with Duffy, aged 32, earlier this month after being impressed by his performances during the first-half of the Championship campaign.
Wilder, whose side face Preston North End in the fourth round of the FA Cup on Saturday, expects an announcement to be made shortly.
“Mark has made it absolutely clear that he doesn’t want to go anywhere,” he said. “We want him to remain with us and so I don’t see there being any problems. I’m expecting it to get done and dusted pretty quickly.
“I think it’s important that people are rewarded when they do well, which Mark has, and it helps to create the right sort of environment.”
Wilder has made securing the futures of United’s leading names one of his top priorities since being appointed 20 months ago, with John Fleck, Billy Sharp, Chris Basham and Jack O’Connell among those awarded new deals. Duffy, a free signing from Birmingham City, was a member of the squad which lifted the League One title last term and has made 25 appearances so far this season.
Goalkeeper Simon Moore is expected to become the next player to open discussions after regaining his place in the starting eleven.
Although United have signed four new players during the transfer window, including Charlton Athletic’s Ricky Holmes, Wilder insisted: “Getting things like this nailed down are just as important as bringing new people in, even more so in a sense, because we are looking to build and plan properly.
“In the past, I can remember coming to a game here and there were about 40 or so people on the back of the programme, which was too much, and also knowing that a lot of them were going to come out of contract at the same time. That’s not a situation we want to be in again or should be.”