It's understood that Muscat's name is among several foreign and Japanese coaches in the mix to succeed Takafumi Hori at the J1’s best-supported club.
Hori, who led the Reds to AFC Champions League glory in 2017, was dismissed on Monday after three losses and two draws from the opening five matches of the new J-League season.
And with former Socceroos coach Ange Postecoglou already occupying the hot seat at J1 rivals Yokohama F. Marinos, his Victory predecessor now finds himself in the frame to possibly follow his mentor's footsteps to Asia's most prestigious league.
Muscat signed a two-year contract extension with the three-time A-League champions in mid-March and the interest from Urawa, who last month completed the signing of former Victory winger Nabbout from Newcastle Jets, is a complement to the progress made by the 44-year-old.
Muscat boasts the A-League's second-best winning percentage, and hasn't missed the finals since succeeding Postecoglou in 2013 as Victory coach.
He led the Victory to the 2014-15 premiership-championship double and they are placed fourth this season and locked in for the finals with two rounds remaining.
News of Urawa's consideration of Muscat comes on the eve of his side's crucial Group F ACL clash against Ulsan Hyundai in South Korea on Wednesday night.
Both sides are on five points after four games, and chasing second spot in the group behind a dominant Shanghai SIPG.
Urawa, beaten 2-1 by Jubilo Iwata on Sunday, have installed youth director Tsuyoshi Otsuki in temporary charge while they source a new coach.
It was a swift fall from grace for Hori, with the 50-year-old named the AFC's 2017 coach of the year back in November, after leading the club to their second ACL crown.
He was in his second spell in charge, having taken over from sacked Serb Mihailo Petrovic in July.
Urawa are currently one off the bottom of the J-League standings.
The World Game approached Victory's football operations manager Paul Trimboli for a comment on Wednesday.