Leeds are considering sacking Javi Gracia after just two months in charge, according to reports, with Allardyce said to be among the names in the frame to replace him.
Gracia was appointed as Jesse Marsch's successor in February, on a deal until the end of the season, with Leeds in the bottom three at the time.
Former Watford boss Gracia won three of his first six games in charge as Leeds climbed to 13th.
But Leeds' terrible April - which saw them lose successive home games to Crystal Palace and Liverpool 5-1 and 6-1 and concede 23 goals - has left them perilously close to the relegation zone.
After Sunday's 4-1 defeat at Bournemouth, Leeds are now 17th and just outside the bottom three on goal difference ahead of Saturday's visit to leaders Manchester City.
A daunting run-in also includes home games against Newcastle and Tottenham and a trip to West Ham.
Former England manager Allardyce has emerged as a strong contender to succeed Gracia at Elland Road should the Spaniard be sacked.
The 68-year-old has been out of football since leaving West Brom in May 2021 following his first top-flight relegation.
Lee Bowyer, who made 265 appearances for Leeds between 1996 and 2003 and has managed Charlton and Birmingham, has also been mentioned as a possible short-term replacement.
Director of football Victor Orta, who joined the club from Middlesbrough in 2017, is also reportedly set to leave Elland Road