The Blades have this summer added Phil Jagielka and record £5m signing Luke Freeman to the squad that won promotion last season.
But Wilder wants to strengthen further with Swansea City striker Ollie McBurnie and Neal Maupay, the Brentford forward, both high on his wishlist.
Dean Henderson is also wanted back on loan from Manchester United, while Ravel Morrison has impressed on trial and could be offered the chance to play a part in United's first campaign at the top level for a dozen years.
"We are deep in negotiation with four or five players," said Wilder earlier today to 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."
On the quest to bring in new faces, Wilder added: "I should imagine we will break our transfer record a few more times, that is the division we are in. But these people have been on the list a long time. They are good players and they're coveted by other clubs as well. But I think we're an attractive club."
Morrison, who started at Old Trafford before moving to West Ham United, has missed training for the past couple of days with a heel injury. It meant the 400 or so fans who attended the club's open training session this morning were denied the chance to see a player who was once touted as a potential England international.
The injury is likely to see Morrison also miss out tomorrow night as the Blades tackle La Liga outfit Real Betis in Faro.
Sources have suggested United could be in a position to announce their third summer signing ahead of that first pre-season friendly.
On Morrison, Wilder added: "I am really disappointed that people haven't seen Rav. He has been really good. We have enjoyed him being with us.
"We are looking to explore that one and see how it goes. But he has impressed everyone. The recruitment, that is where we are and we sometimes have to go down that road.
"He is enjoying it, we have spoken to him and him coming in, the way he arrived, that was a box ticked from our point of view. It is nothing major, he has just got a sore heel and, hopefully, he will be involved. It wasn't the be all and end all, though, that he was involved in the game. It was other things we wanted to look at."
Wilder, fresh from signing his new three-year contract, took part in an impromptu Q&A session with supporters on the pitch after today's training session had been completed.
Players and staff then mingled with fans for an hour or so, further strengthening the bond that has been created since Wilder took charge.
"These fans are the lifeblood of the club and it is great to see so many make the trip," added Wilder, who is expected to start both Jagielka and Freeman tomorrow night against Betis.