The 54-year-old has not taken up a new managerial role since leaving the Blades in March, when the club were bottom of the Premier League.
Middlesbrough's win over Cardiff on Saturday afternoon spelt the end for Barnsley-born manager McCarthy, who had suffered eight-straight defeats.
Wilder has previously been linked with the West Bromwich Albion job, a vacancy that was filled by ex-Barnsley boss Valérien Ismaël during the summer.
Wilder guided Sheffield United into the Premier League in the 2018-19 season and oversaw a fine first season back in the top flight as the Blades finished ninth in the table to secure their best league position for almost three decades.
However, United struggled in their second top-flight campaign under Wilder, as he left the managerial post at Bramall Lane in March.
Previously, he had successful spells at Northampton Town and Oxford United and took charge of more than 300 games at Halifax Town before the club went into liquidation in 2008.
Next Cardiff manager odds (correct as of 11pm, 23/10/21):
Chris Wilder 2/1
Jody Morris 3/1
Neil Harris 6/1
Michael Flynn 7/1
Steve Morison 12/1
Alan Pardew 16/1
Alex Neil 16/1
Craig Bellamy 16/1
Eddie Newton 16/1
Mark Hudson 16/1