The Welsh club are hovering above the relegation zone following Saturday’s 3-0 home defeat to Leicester, and the Mirror claims that Monk’s time at the Liberty Stadium is up.
Huw Jenkins is apparently ready to part ways with the 36-year-old before next weekend’s trip to Manchester City, and has already held talks with former Everton and Manchester United boss Moyes about taking charge.
The Scotsman is available for work after being sacked by La Liga outfit Real Sociedad last month and could be tempted by a Premier League return after failing to succeed at Old Trafford.
Swansea are in trouble after winning just one of their last 11 league games despite signing the likes of Andre Ayew during the summer, and are just two points ahead of 18th-placed Sunderland.
However, the report adds that Swansea face stiff competition to land Moyes’ signature.
It is believed that the 52-year-old is a wanted man, with Steve Parkin looking to bring him to Leeds if an Elland Road takeover is completed.