The Daily Mail claim Chris Wilder will likely return to Bramall Lane if Heckingbottom is dismissed from his position.
Wilder was successful during his managerial stint at the club between 2016 and 2021.
The Blades were competing in League One at the time of his appointment, but he took them to the Championship before securing them Premier League promotion in 2019.
The pressure on Heckingbottom is increasing with Sheffield enduring a miserable run of form in the English top flight.
They have lost eight of their nine matches and are bottom of the standings.
Their latest defeat came at the weekend against Manchester United, with goals in either half from Scott McTominay and Diogo Dalot ensuring the away team’s 2-1 success.
The Blades appointed Heckingbottom as their first-team manager in November 2021 following Slavisa Jokanovic’s dismissal.
The English boss led them into the playoffs by May, but a semi-final defeat to Nottingham Forest ended their hopes for Premier League promotion.
However, the 46-year-old achieved that feat last season, guiding his side to a second-place finish to secure automatic promotion from the Championship.
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