Speculation about the centre-forward's future continues, with Leeds United one of those linked with their former player.
And while Wilder maintains the decision is the 33-year-old's, he says he has not talked to Sharp about it for weeks.
“I spoke to him about three weeks ago about it (Sharp's future) knowing what was going to come up and that the question was going to be asked, and rightly so. If I was in the Championship and needed someone to give us a boost and saw Billy wasn’t playing at Sheffield United, I’d ask the question (about whether he was available).
“But Billy's got an important part to play and he's had an important part to play because he's put huge pressure on Lys Mousset, Oli McBurnie and Callum Robinson. How good is it for them to learn from the likes of Billy and (David) McGoldrick?
“The example he’s setting and the influence he has on the players coming up from the Championship is huge.
“But the decision is with Bill. If he comes to me and says he needs to go, of course I'll respect that.
“If I was a top Championship club trying to get into the Premier League and needing a few goals, I'd ask the question but we’ll need him too before the end of the season. Our need is a greater one, or as great as those clubs in the Championship.”
Although Sharp scored the Blades' first goal back in the Premier League, an 88th-minute equaliser at Bournemouth on the opening weekend, his role as largely been as it was then, to make an impact from the bench. He has not scored since, although he came extremely close at Manchester City, his header hitting the post and rolling across the goalline.
His two starts this season came at the League Cup in August, and at home to Newcastle United in December. He has come off the bench ten times, and was an unused substitute at home to Fylde in the FA Cup third round, even with manager Wilder making 11 changes. He is likely to be a substitute again in Friday's Premier League game at Bramall Lane.
Leeds are in the market for another striker after Arsenal recalled Eddie Nketiah from his loan spell, unhappy at the amount of game-time the striker had in the first half of the season. The budget at Elland Road is tight, however, and they also need to consider whether they require more experienced cover for goalkeeper Kiko Casilla, who has been charged with using racist language in November and could receive a ban if he is unable to successfully contest the accusations.
Sheffield United are also looking to add to their squad, to provide greater depth. Their outside centre-backs and wing-backs have been Premier League ever-presents, but the Blades went into the window feeling they needed to up the quality of their potential stand-ins, while Wilder is a manager who constantly likes to refresh his attacking options.
So far they have signed Jack Rodwell, who made his debut as a central defender on Sunday, but can also play a variety of midfield roles. Rodwell joined as a free agent, but prising players from other clubs is proving more difficult.
Wilder feels he has to play his cards close to his chest.
“We can’t get involved in an arm wrestle with anyone, West Ham and a few clubs have been doing that but we haven’t the ability to and I wouldn’t do it like that anyway,” he commented. “We have targets and positions we need to cover and we’ve got a budget I’ll try to maximise.
“If you come at me with names I will bat them off Boycott-style. I appreciate it's a big part of what happens in the media, and it's very interesting for everyone, I like watching it but not fielding the questions.”
The names of those players Wilder is looking to move out perhaps gives a clue as to what else he is looking to bring in.
“Richard Stearman, Kean Bryan, Jake Wright (all central defenders though Wright can also play at left-back), (centre-forward) Leon Clarke and Ben Heneghan (another central defender) need games,” said Wilder. “If we receive bids for anyone we’ll assess them and do what’s right for the club.
“We've got positions we need to strengthen but we'll not bring in four to six players because the group in a good place at minute. It's just a tinker, but it's an important window.”
Stearman has been linked with Huddersfield Town, Bryan with Charlton Athletic.
Jake Eastwood has been recalled from a loan at Scunthorpe United in the light of a short-term injury problem in goal, but could go out again when it clears.
Second-choice Simon Moore is back in training after picking up an injury in mid-December, but Michael Verrips will sit out the West Ham game because of an injury picked up on his Sheffield United debut, against Fylde.