Of the eight U’s players whose deals ended this summer, only Adam Chapman, Asa Hall and Wayne Brown were offered the chance to stay when the decisions were made this week.
Paul McLaren, Mark Wilson, Oli Johnson, Anthony Tonkin and Aaron Woodley were all released.
The successful trio were due to receive the formal details yesterday after being told of the club’s plans in meetings on Tuesday.
United are keen to complete the process as swiftly as possible, giving them the maximum amount of time to search for transfer targets during the close season.
Wilder is optimistic all three will put pen to paper, despite the possibility of interest from other clubs.
He said: “The offers going out are sensible, it’s nothing ridiculous in terms of where we’re at, there’s not a massive injection of money.
“I’m not going to put a gun to their heads, but I won’t hang on forever and they know that.
“Fingers crossed, we can get it tied up with their agents pretty quickly.
“I can’t do anything about other clubs, but I think they would be daft to leave us because we think the progression of the club is there for all to see.
“I spoke to them on Tuesday and I’d be very surprised if they didn’t stay.”
If Brown agrees a new deal, his role will include coaching.
The 35-year-old will continue to deputise for Ryan Clarke, but would work alongside goalkeeping coach Alan Hodgkinson, who turns 76 this summer.