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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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
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