United have lodged a bid – understood to be £5m – for the Ipswich Town forward although they face competition from Middlesbrough before Thursday’s deadline for permanent deals.
If successful it would be the Blades’ sixth signing of the summer after Manchester City’s Kean Bryan yesterday followed Liverpool’s Ben Woodburn in arriving at Bramall Lane.
On Waghorn, Wilder said: “The deal is out there. We have put a bid in for him and it’s there.
“We feel it is a reasonable fee, we are not frightened and afraid to be aggressive, go after people and spend.
“We broke the club record fee for John (Egan), but we won’t get sucked into silly stuff.
“We have got other situations, but we just have to be patient and see what falls.
“We need competition at the top of the pitch, and we are looking to bring one in. We’d like to do it sooner rather than later.”
United have sold Wales international David Brooks to Bournemouth – for a reported £11.5m – but have managed to keep the majority of their squad intact.
Wilder said: “We have had to be patient, but I think we have had a fantastic window.
“We have brought in two great loan signings – Dean Henderson from Manchester United and Ben Woodburn from Liverpool – two frees in David McGoldrick and Kean Bryan, and John Egan, who has played in this division and who we broke our club record fee to sign.
“We are delighted with all our business and, on top of that, keeping hold of the likes of (John) Fleck and (Jack) O’Connell.
“We are in a position to use the increased budget we have got since last year – we have hardly touched the David Brooks money – and I think we are in a great position. That’s a skill, allows us to grow, improve and bring better players into the football club,” added Wilder.
England youth international Bryan, 21, yesterday signed for United on a free transfer although the deal includes a hefty sell-on clause and buy-back option. “We watched Kean throughout last season and he’s got a great pedigree with England and Manchester City,” said Wilder.
“It’s a fantastic deal for us. Kean is naturally left-footed, he can play left centre-half, left-back and in midfield and he is a very good technical player we think we can develop.”