But while lavish signings cannot be expected, Wilder has warned those looking to sign his best players they will not be allowed to leave for anything less than their market values.
To re-sign Henderson for a third season-long loan from Manchester United would be a huge coup. Along with Burnley's Nick Pope, the 23-year-old is fast challenging Everton's Jordan Pickford as the best English goalkeeper.
Wilder insists the free signing of Wes Foderingham from Rangers, announced this week, is part of a wider rejig of the goalkeeping department and not an indication that a decision had been made on Henderson.
The transfer window opens in July 25, the day after the 2019-20 season ends, and Premier League clubs must have their business done by October 5. There is as yet no start date for next season, but the feeling is it could be September 12, so the Blades will want to know as soon as possible if they need to replace their first-choice goalkeeper.
"Dean and Manchester United know our thoughts on the situation," commented Wilder.
"We've already started talking to the player and Manchester United, while respecting it's their decision and the boy's decision.
"We would love to extend it for another season, and when we get the news on that we'll let you know."
Henderson and his Manchester United manager Ole Gunnar Solskajer have already made their views on his long-term future plain. Solskjaer sees him as a future No 1 at Old Trafford, and Henderson does not want to return as anything less.
Luke Freeman, Callum Robinson, Lys Mousset and Oli McBurnie all pushed back the club's record transfer fee last summer before Sander Berge set a new mark again at £23m.
With the impact of coronavirus keenly felt across football's finances, Wilder has warned supporters the emphasis this time will be on free transfers like Foderingham's.
"It will have to be,” he said. "The chief exec (Stephen Bettis) will be talking about budgets and where we are, really, going forward in discussion with the board so, as always from my point of view, it's about getting the maximum out of what is available.
“I don't think there's going to be any head-turning transfers from our point of view so we'll have to work hard to improve the group, which we've always tried to do. We're confident it'll be a stronger group at the start of next season as it was at the end of this one.”
The Blades have lost some top talent in recent years, with the likes of Harry Maguire, Kyle Walker and Dominic Calvert-Lewin establishing themselves as leading Premier League players.
John Egan and Chris Basham are yet to sign new contracts after attracting interest from elsewhere, but the Blades are most vulnerable over John Lundstram, who is in the final year of his deal after the club triggered an extension.
Whereas they were a Football League club when Maguire, Walker and Calvert-Lewin were picked off, they can afford to hold out for higher prices now for players who have proven themselves in the top division.
"No one is going to put a gun to our head to accept small offers for players we rate and value," insisted Wilder.
"It will be market value if anything happens, but no one has picked up the phone to me and I’m sure Steve would have told me if anything had happened.
“I think we are still a selling club, but we are a more powerful one. We are in a better position on the pitch.
“We can attract better players now. We’ve always attracted players because of the size of the football club and history.
“From a wages point of view, from a financial point of view, if any of the big clubs did come calling for any of our players, I can’t stand in their way. And although we’re in a better position, it’s still difficult if anybody wants to double a player’s wage and stuff like that.
“I’m jut being realistic but we have more control."
The Blades could also have the carrot of European football.
They go into Monday's Premier League match against Everton two points behind sixth-placed Wolverhampton Wanderers. Finishing sixth would guarantee a first European campaign in the club's history, and seventh would put them in the Europa League if Arsenal are beaten in the FA Cup final.
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