The 22-year-old goalkeeper has spent the 2018-19 campaign on loan at Bramall Lane.
His efforts have helped the Blades to promotion, with the club preparing for life back in the Premier League.
Henderson has stated his desire to form part of Chris Wilder’s plans in the top tier and an agreement to make that dream a reality is close.
Sheffield United have already held initial talks with their counterparts at Old Trafford and are optimistic when it comes to getting a deal done.
"We went over there, [assistant manager] Alan Knill and I, to watch the Manchester derby," Wilder told the Sheffield Star.
"We've got a really good relationship with them, they're great to work with, and we saw John and Ed Woodward.
"We talked briefly about Dean. Manchester United are keen and we are keen. He (Henderson) has made all the right noises."
While expecting to have Henderson back on his books next season, Wilder concedes that the England U21 international is likely to join on a short-term agreement.
He added: "He's a Manchester United player and there's not talk of a permanent. We believe it will be a loan.
"Hopefully we can get it wrapped up as quickly as possible because there's an enormous amount of work to do, not only on the pitch.
"Hopefully we can get it done. Then that's one, of many things, we'll have ticked off."
Henderson has made no secret of his desire to link up with the Blades again, or his ambition to one day make the grade at Old Trafford.
He has told BBC Radio Sheffield: “Listen, I want to be here.
“I want to play Premier League football at Bramall Lane. Eventually, I want to be Man United’s number one and England’s number one.
“But, at the end of the day, the love this club has shown to me. You want to feel loved, you want to feel welcomed. And I’ve never felt so welcomed in my life. Everywhere I go in Sheffield, people give me hugs, take pictures, everything.
“I’ll be honest with you, it made me really emotional to get this club back where they belong. It’s a massive football club, and driving forward. They deserve to be in the Premier League.”