The Red Devils are currently on the lookout for a new manager after Dermot Drummy left the club by mutual consent early in May.
Former Liverpool, Leeds United and Australia winger Kewell, meanwhile, left his role as Watford's Under-23 coach in April, and is reportedly keen to launch his managerial career.
According to The Argus, Crawley owner Ziya Eren is willing to take a gamble on another inexperienced manager in Kewell, having appointed former Arsenal and Chelsea academy coach Drummy 13 months ago to replace Mark Yates.
It would be the 38-year-old's first job in senior management since calling time on a glittering playing career three years ago which saw him win the Champions League and FA Cup with Liverpool.
Crawley finished 19th in League Two this season, winning just one of their last 14 games.