The 44-year-old was relieved of his duties following Preston's 3-1 defeat to Yeovil Town on Tuesday, with the club just five points above the relegation zone in League One.
However, according to BBC Sport, Preston expect to have a new interim boss in place by Thursday.
A statement from the club on Wednesday read: "Graham oversaw a fundamental change in reducing the wage bill in line with the financial fair play criteria and brought together a whole new squad of players last summer.
"After an initially encouraging start to the season regrettably results have not been acceptable and the board felt that a change of manager was the only way forward. Graham leaves with our thanks and best wishes for the future."
Westley took charge of Preston in January 2012.