That’s according to Peterborough United chairman Barry Fry, who made the claim during an interview with Football Fancast.
Wilder left his job at Bramall Lane last month after five years in charge, with the Blades currently rooted to the foot of the table.
Despite having spent the entire season embroiled in a relegation battle, United failed to bring in any reinforcements for the second half of the season, but Fry believes that the decision to leave things how they were was not Wilder's.
He said: “There came a time, I think in December, that he felt that that no matter what he did, he couldn’t keep this group up.
"I think he felt to be fair to the fans, to the club he loves, he’d offer to resign.
“Also in December, and early January, I’ve been told that he requested three players in the window, and the board refused to back him on any, which is fair enough, because they’re going to get relegated, and they’ve got no income coming in.”
According to Transfermarkt, Sheffield United spent £56.4 million last summer, signing the likes of Rhian Brewster from Liverpool, Aaron Ramsdale from Bournemouth, and Oli Burke from West Brom.
Elsewhere, Football Insider claim that Crystal Palace are considering a move to lure Sean Dyche away from Burnley this summer.
Roy Hodgson’s contract expires at the end of the season, and it is understood that the Eagles have already made contact with Dyche, who is keen on accepting a new challenge.
We’ve gathered the rest of today’s Premier League transfer rumours below: