Former Rangers and Scotland star Ally McCoist has suggested that Wilder won't be named as Celtic's next manager at the end of the season, despite being the bookies' current favourite to land the job.
The 53-year-old's departure from Bramall Lane was confirmed last weekend, bringing to an end a five-year spell that saw him take the Blades from League One to the Premier League.
When asked by talkSPORT Breakfast Show host Alan Brazil whether he believed Wilder would be given the vacant position at Celtic, McCoist claimed: “I never even thought about that, mate... you've thrown that one at me! No, I don't think so.
“I tell you why, because I think Celtic are probably further down the line with somebody prior to Chris Wilder losing his job at Sheffield United.”
Meanwhile, former Sunderland ace Darren Bent chipped in with his assessment of Wilder's exit, and said: "Yeah, the Sheffield United one is strange, but that's the evolution of football - unfortunately, people don't want manager anymore, they want head coaches, and chief executives and people above overseeing the buying of players.
“For Chris Wilder, he's been unfortunate enough to be caught up in it, but the Sheffield United fans I've spoken to about it are devastated, absolutely devastated.”
As always, however, there is still plenty of talk surrounding transfers!
Here, we take a look at the rest of the transfer talk from the Blades and their top-flight rivals:
When asked by talkSPORT Breakfast Show host Alan Brazil whether he believed Wilder would be given the vacant position at Celtic, McCoist claimed: “I never even thought about that, mate... you've thrown that one at me! No, I don't think so.
5. Leeds eye defender
Leeds United are maintaining an interest in Torino and Cameroon centre-back Nicolas N'Koulou. (Mail)
Photo: Marco Luzzani
6. Leeds target left-back
Ludwig Werder Bremen left-back Ludwig Augustinsson is a possible summer transfer target for the Whites. The report states Augustinsson would be available for a seven-figure fee, should Leeds renew their interest. (Kicker)
Photo: Pool
7. Josh Doig wanted by Leeds
Hibernian defender Josh Doig is another option at left-back for Leeds, with reports suggesting that the youngster could be available for just £1.5m this summer. (Daily Mail)
Photo: Mark Runnacles
8. Simpson on trial
Former Leicester and Newcastle right-back Danny Simpson is on trial with Championship side Sheffield Wednesday as he bids to find a new club after leaving Huddersfield last summer. (Leicester Mercury)
Photo: Nathan Stirk