The 32-year-old linked up with the Blades on a short-term deal in August after leaving Championship rivals Middlesbrough at the end of last season.
The former Barnsley captain has started just two league games for Wilder’s side, but offers versatility across the backline for promotion-chasing United.
The dressing-room influence of Cranie – who has been involved in squads fighting for promotion to the Premier League for the past two seasons – is also not lost upon Wilder, with his desire to persuade the Yeovil-born player to commit for the rest of the season being two-fold.
On Cranie, promoted with Huddersfield Town in 2016-17 and part of the Boro squad who reached the play-offs last season, Wilder said: “Martin is an excellent professional and has been a valuable member of the squad this season.
“He is zero maintenance, he just comes in and works hard and when called upon, he has been ready and let no-one down.”
Meanwhile, Wilder is not yet ruling out another vastly-experienced defender on the club’s books in Jake Wright from making a key contribution this season – should he remain at United and not move elsewhere.
Wright, 32, who recently saw a move to Scunthorpe United fall through, is the subject of further lower-division interest and is still expected to leave this month.
Young Blades defender Callum Semple, 20, is set to continue his loan education in League One or League Two following a successful loan spell north of the border with Queen of the South.
Fleetwood manager Joey Barton has been fined £2,000 by the Football Association for comments he made about referee Brett Huxtable.
Barton branded the performance of Huxtable and his fellow officials as the worst he had seen in his entire career following a 2-1 defeat at Bristol Rovers.
The FA last week handed Barton a two-match touchline ban after the former Manchester City, Newcastle and England midfielder was sent to the stands at the Sky Bet League One game on December 22.
Barton criticised Devon official Huxtable following a Memorial Stadium clash that saw Fleetwood striker Ched Evans sent off and 11 players booked.