The Sunday Telegraph reports that Moyes could replace Steve McClaren who is nearning the exit door at Stamford Bridge.
The Magpies are expected to sack McClaren following the club’s fifth defeat in six matches, after they lost 3-1 at home to Bournemouth.
Moyes has been out of work since he was sacked by Spanish side Real Sociedad in November.
Newcastle are one point from safety with 10 games remaining.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.