Goalkeeper Foderingham joined the Blades on a free transfer on Friday after leaving Rangers in May, while Henderson has been on loan from Manchester United for the last two seasons.
Wilder is keen for 23-year-old Henderson to extend his stay at Bramall Lane, and that has not changed in light of Foderingham’s arrival.
“Dean and Manchester United know our views on that, we already have started talking to the player and Manchester United,” Wilder said.
“It is their decision and the boy’s decision. We would love to extend that for another season and when we get the news on that decision we will let you know.
“Wes was available, we needed to strengthen that department, there will be a couple of changes going forward in that department. He became available, a free transfer and a three-year deal.”
Sheffield United are still in the hunt for a place in the Europa League next season after an impressive first term in the Premier League in over a decade.
The Blades are eight in the standings on 54 points with two games remaining – two points behind sixth-placed Wolves.
Wilder’s side host Everton on Monday before wrapping up the season away at Southampton on 26 July.