The Blades have this summer brought in former England defender Phil Jagielka and QPR wideman Luke Freeman, the latter in a £5m deal that eclipsed the previous record set a year earlier when John Egan arrived.
Wilder, however, wants more with Swansea City striker Ollie McBurnie and Neal Maupay, the highly-rated Brentford forward, both on his wishlist, while reports in Lancashire suggest United have had a bid accepted for Preston’s Callum Robinson.
United also want to bring back Dean Henderson on loan from Manchester United, while the indications are that former West Ham United midfielder Ravel Morrison will be offered a contract following a spell on trial.
“We are deep in negotiation with four or five players,” Wilder told The Yorkshire Post at the club’s training camp in Portugal.
“The work we have done has ramped-up. It has been tireless. The same old thing, it is difficult to mention names. But if we get them great. If not, we move on. What I can say is we have worked ever so hard.
“I know it is frustrating. Football fans up and down the country want to see new players in the shirt and signing contracts.
“But the situation is we are working really hard and we are really confident we can add to the group. We know we have to. We are close.
“I would love to get two or three in by the middle of next week. And then get them into the games. I knew it was not going to be done in the first week but, hopefully, we can bat on with this and all the hard work gets rewarded.”
With McBurnie and Maupay both rated at £10m-plus by their clubs, the likelihood is that the £5m fee paid to QPR for Freeman last month will soon be broken. “I should imagine we will break our transfer record a few more times,” added Wilder, who earlier this week signed a new three-year contract.
“That is the division we are in. But these people have been on the list a long time.
“They are good players and they are coveted by other clubs as well. But I think we are an attractive club.”
Henderson is understood to be keen to return to Bramall Lane after enjoying last season’s stay. Manchester United are also believed to be happy with the move, suggesting an agreement could be struck soon.
As for whether Morrison, who started his career at Old Trafford, will be offered a deal at the end of his on-going trial, Wilder added: “He has been really good. We have enjoyed him being with us and he is enjoying it.
“We are looking to explore that one and see how it goes. But he has impressed everyone.”