Loan signing Henderson, 22, proved a huge success this term as the Blades finished runners-up in the Sky Bet Championship to end a 12-year exile from the top flight.
Henderson kept 21 clean sheets to win the Championship Golden Glove award, and said after the Blades won promotion that he wanted to return to Bramall Lane next season.
Manchester United’s own goalkeeping situation remain uncertain, with doubts over the future of Spain star David De Gea, but manager Ole Gunnar Solskjaer appears to be open to the idea of again loaning out his England Under-21 international.
“We’re working our way through it,” Wilder told Press Association Sport over the ongoing Henderson talks.
“We’ve been in discussions with Manchester United and I think they see it as a positive that he gets a year of Premier League football under his belt.
“I know Dean definitely wants to stop and our supporters absolutely adore him.
“We’ve got a good relationship with Manchester United and if Dean signs we’ll be delighted.
“He’s been outstanding since he’s been at the club. He had a fantastic loan period at Shrewsbury, he’s kicked on and has a wonderful future ahead of him.”
The Blades secured a surprise promotion to the top tier just two seasons after being crowned League One champions.
Wilder’s squad is made up of entirely British and Irish players and the 51-year-old, who was named the League Managers’ Association Manager of the Year, does not envisage change as he prepares to embark on the biggest challenge of his career.
“These are the players I know the best,” said Wilder, who has won promotion to all four divisions in the English Football League.
“We’ve not dipped into the foreign market and that’s not to say that down the line I wouldn’t.
“But I trust this group of players and I trust my own eye in terms of the players we’ll bring in. It’s worked for us.
“Nuno (Espirito Santo) at Wolves signs Portuguese players, David Wagner at Huddersfield signed German players. I don’t think I’m bucking the trend in any way, it’s just players I know and trust.”
United are preparing for top-flight football for the first time since their controversial relegation in 2007 following the Carlos Tevez affair when rivals West Ham broke rules on third-party player ownership.
The Premier League has become more cosmopolitan and wealthy in the dozen years since, but Wilder promises to continue his pragmatic transfer approach, with Swansea striker Oli McBurnie and Brentford’s French marksman Neal Maupay emerging as early summer targets.
“I think there’s a nice balance (to be found) between a couple of the clubs who were promoted last year,” Wilder said.
“Fulham made wholesale changes and ripped the heart out of the team and Cardiff had nine out of the 11 who played in the Championship and came very close (to staying up).
“We want to keep the backbone of the team, the heartbeat of the team, because they deserve an opportunity as well.
“We have to add obviously, but we want to add some young players that will relish the opportunity of playing in the Premier League.
“There’s a lot of good players in the Championship that can go really well in the Premier League. We have to spend our money wisely, but we think we’ll be an attractive proposition for players.”