A report in the national press claimed the veteran boss, now 73, is ‘on the radar’ of Barnsley, who are eight points adrift at the bottom of the Championship table.
Warnock left Middlesbrough in Novemeber but is keen to return to the dugout.
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He previously saved Rotherham United from Championship relegation under similar circumstances in the 2015/16 season.
Speaking to BBC Radio 5 Live last week, Warnock, who spent eight years in charge at Bramall Lane from 1999 to 2007, said: “Somebody asked me the question ‘Would I go back into any club between now and the end of the season?’ and I said ‘Yes’."
Barnsley are yet to win in 10 league matches under former Sweden under-21 boss Poya Asbaghi and face Luton Town on Tuesday.
The club was hit with an FA charge along with Cardiff City on Monday following heated scenes at the final whistle during their game at Oakwell last week.
A brawl involving players and staff erupted in the tunnel after the Reds’ assistant coach Joseph Laumann appeared to shove Cardiff manager Steve Morrison.
Elsewhere, Derby County boss Wayne Rooney believes his side could face another final-day-of-the-season decider in their bid to escape the drop from the Championship.
The Rams are seven points from safety after being deducted 21 points by the EFL.
Rooney said: "It might be the last game of the season again, you never know, but all we can do is keep working, keep trying to pick up points and give ourselves the best chance we possibly can."