High on the list of his priorities is replacing Wales international David Brooks, who left for Premier League side Bournemouth earlier this month.
United are also tracking another striker, although the prospect of Ipswich forward Martyn Waghorn arriving in South Yorkshire looks unlikely after Wilder admitted there is a difference of opinion over his value.
“I believe we’re two players light,” said Wilder, who last season led the Blades to a tenth-placed finish in their first season back in the Championship after a six-year absence.
“We need to replace Brooks and we need to bring another centre-forward in to give us the four that we require.
“We’ve got three and they’re all different types of strikers.
“We’re working hard on it.
“We have to kick on, bridge the gap and not rest on our laurels.
“We all enjoyed the journey last year and I want us to do that again this season.”
When it comes to working the transfer market, reputations count for precious little at Bramall Lane these days.
In previous years the Blades have targeted big names, many with their best days behind them.
The club’s previous record signing, up until this week, was James Beattie who arrived in 2007 as a bona-fide Premier League player with England caps to his name and big wages to boot.
Such an approach was never going to suit the style of Wilder.
The current incumbent in the United hotseat takes a more sensible approach to recruitment than his predecessors.
He pores over potential acquisitions and prefers to search for talent in the second and third divisions.
That point was emphasised when John Egan surpassed Beattie as the club’s record signing on Monday.
Egan’s arrival from Brentford perhaps sums up how the club have moved on in the past decade, and especially since Wilder arrived two summers ago.
Egan is 25, a central defender and has just two full seasons in the second tier under his belt.
He has been signed not because of what he has done in the past, but because of what he is capable of achieving in the future and, more importantly, while wearing a United shirt.
The club’s recruitment policy is there for all to see.
The squad is full of young, hungry players and not burdened with professionals that have laboured around in the top flight for too long.
Wilder has moulded a squad that plays attractive football and the 50-year-old is adamant his club will not sign players purely because of their perceived prestige.
“Players that we’ve got get written off because they aren’t names that are in the headlines,” he said.
“But a lot of clubs get sucked in just off players’ names and reputations and what they’ve done before.
“They can pay over the odds and pay big transfer fees and big wages.
“It’s not about just getting in fashionable footballers or players that are in vogue.
“I don’t give a monkeys where I get my players from, as long as they run around and do the business.
“We have to be clever and have to find players from different areas.”
Another recent acquisition, David McGoldrick, perhaps typifies that approach best.
McGoldrick is not a household name but hours after signing a deal he notched a well-taken goal against three-time European champions Inter Milan in a friendly this week.
He has impressed since arriving on trial with his commitment to the cause.
The fact that he was signed on a free further highlights Wilder’s belief in looking at every outlet for potential additions.
The United chief believes his latest signing not only fits the club perfectly but also has the right attitude to prosper in an already-close group of players.
He also hopes McGoldrick can avoid the types of injuries that a lengthy commute causes.
The 30-year-old was regularly driving between his family base in Nottingham down to previous employers Ipswich.
“David’s come in and I believe it’s a good fit,” said Wilder.
“We’re still a relatively young Championship side but he’ll help us with his experience.
“He’s a centre-forward who gives us something a bit different.
“I think some of the niggles he’s had over the last few years are from being sat in a car for four or five hours, three times a week.
“Now he’s back home and is close to Sheffield.
“We offered him a deal that represents really good business from our point of view.
“He has to hit some games to get a second year and it comes within our wage bracket, which is structured and doesn’t get out of hand and out of control.”