The 22-year-old played a key role in helping the Blades win Premier League promotion during the 2018/19 campaign, featuring in every league game.
Old Trafford boss Ole Gunnar Solskjaer is happy for the keeper to return to Bramall Lane next season to gain experience in the top flight, according to the Mirror.
Henderson’s current deal with the Red Devils is set to expire next summer, but the club want to tie him down on new terms.
Sheffield United manager Chris Wilder was confident of getting the deal done.
“Dean made it clear to us that he has a very strong interest in coming back to Bramall Lane, and Manchester United are happy to go along with that,” he said.
“He wants his United contract sorted out first of all but, in terms of putting another temporary deal in place, I think we’re in a good place with that one.
“United are pleased with what happened when he came here, with the way his game developed and the way he progressed over the course of the year.
“He’s rated very highly at Old Trafford and you can understand why. Dean was outstanding for us last season and being able to bring him back again for another year would be brilliant.”
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