Allardyce was appointed on a short-term deal with four matches left of the Premier League season in the hope of helping the club to avoid relegation.
However, he was unable to do so, as Leeds were relegated back to the Championship after three years in the top flight.
According to the Daily Telegraph, the 68-year-old met the club's CEO Angus Kinnear for talks over his future with the decision made to part company.
As a result, Leeds are looking for a new manager to lead them into the new EFL season.
Steven Gerrard is currently the bookies' favourite, with Brendan Rodgers and former Leeds midfielder Lee Bowyer among the other frontrunners.
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Leeds may also be looking for a new director of football following the departure of Victor Orta during the final weeks of the season.
There could also be big changes at boardroom level with uncertainty over Andrea Radrizzani's future at the club after he agreed a deal in principle to buy Sampdoria.
While his plans are yet to be confirmed, he could find himself in an untenable position after offering Leeds stadium Elland Road as collateral when securing a £26million bank loan for his purchase of the Italian club.