Muscat will finish up as Yokohama boss after next Wednesday's Asian Champions League match, completing a successful 2.5-year stint at the J1 League club.
Kewell, who currently works as a coach under Brendan Rodgers at Celtic, is the man primed to replace Muscat, reports Sponichi, despite a difficult start to his coaching career.
If he gets the job, Kewell would be the third consecutive Australian coach to lead Yokohama F. Marinos, following in the footsteps of Ange Postecoglou and Muscat.
It would also be a huge move for the former Socceroos playmaker, who had four senior managerial appointments in England's lower divisions since hanging up his boots in 2014, with limited success - and none since 2021.
Kewell, 45, coached Watford's U23s from 2015-17, then landed his first head coaching role at Crawley Town in 2017.
He was lured to Notts County in 2018 but was sacked after just 14 games.
In 2020, Kewell took over at Oldham Athletic but lasted less than a season before being dismissed in March 2021, with the club sitting 16th in League Two.
His most recent senior coaching job was with Barnet, where he was dismissed in September 2021 after failing to get a win in seven matches at the helm.
Kewell had a brief stint in the coaching wilderness before joined Celtic as Postecoglou's assistant in June last year, determined to learn from the star Australian manager who now leads Tottenham Hotspur.
He will have big shoes to fill in Japan.
Muscat, who is departing for a new challenge, won the J1 League title in 2022, then the Japanese Super Cup this year.
It is unclear where Muscat, who had previously been linked to since-filled roles in the UK at former clubs from his playing days in Rangers and Millwall, will head next.
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