The 32-year-old signed a short-term deal at Bramall Lane until January, and made his first start at right centre-half during Saturday's 1-0 defeat at Nottingham Forest.
The defender's stay in the side may prove to be brief '“Â Chris Basham is available again and expected to retake his place in the side for Friday's Sheffield Derby against Wednesday '“Â but he hopes it proves the catalyst for an extended stay in South Yorkshire.
'One hundred percent, I'll do everything I can in the time I'm here to try and earn a new deal,' the former Barnsley defender said.
'That's obviously down to the manager and staff, but I'll be working hard and will see what can happen.'
Cranie, who helped Huddersfield Town win promotion to the Premier League via the Championship play-offs last May, arrived at United to bolster Wilder's squad after the Blades boss sanctioned the departures of Ryan Leonard and Lee Evans late in the summer transfer window.
His role at right centre-back was a little less all-action than that of Basham, who is tasked with joining in attacks as often as he prevents them, but he barely put a foot wrong against Forest, who eventually prevailed thanks to Lewis Grabban's second-half header.
'We played a slightly different formation without Mark Duffy, but we didn't keep the ball well enough. So it didn't matter who was on the pitch'¦Â it wasn't good enough.Â We'll have to take it on the chin, have a good look at it and get ready for Friday.
'For the fans that's the biggest game of the season and the lads know how important it is, so we'll be working this week to put things right.'
Â Meanwhile, Blades youngster Ben Woodburn has been named in the Wales squad for games againstÂ Denmark and Albania '“Â after Ryan Giggs watched him in a behind-closed-doors friendly against Doncaster Rovers last week.
Woodburn was part of a strong Blades line-up for the game, which finished 5-5. Paul Coutts, Conor Washington, Simon Moore and Marvin Johnson also appeared in the game, at Rovers' Cantley Park training ground.
Former Sheffield United hard man Vinnie Jones will be returning to the Steel City in the New Year.Â He will be the subject of "An Evening With..." at the City Hall on February 9.Â Tickets are from Â£30 and will be available from Thursday on 0114 2789789.