Former Bari forward Farina was sacked after the New South Wales side were eliminated from the A-League playoffs and becomes the 7th coach in 9 seasons to be sacked by the Australian side.
Arnold may be a more cost effective option after recently leaving Japanese side Vegalta Sendai but is reportedly in negotiations with A-League rivals Newcastle Jets.
Although the 39-year-old Del Piero remains a key figure, there are indications that the Italian will play on for another season, although is yet to commit to Sydney.
Del Piero may be considered in a player-coach role, however, he lacks the required coaching certificated but may be given special dispension by the Australian FA.
Del Piero would need to take a significant pay cut from his present 2.6m euro salary should he wish to accept the role.
The former Juve forward has scored 24 goals in 48 appearances for Sydney since leaving the Bianconeri in 2012.