The Hammers are believed to have tried to sign Barkley on loan in January but saw their offer rejected by Chelsea, who were not prepared to part with the midfielder in the middle of the season.
The 26-year-old has been a regular for the Blues during the 2019-20 campaign, making 24 appearances in all competitions, although he has only started 10 Premier League games this season.
According to The Mirror, Moyes is keen on a reunion with a player who he managed at Everton and hopes that the offer of regular football will help entice the England international to the London Stadium.
The report claims that West Ham's head coach wants a 'more mobile' midfield and views the former Toffees youngster as the ideal signing ahead of the 2020-21 campaign.
Barkley has scored four times and registered four assists for Frank Lampard's side this season. body check tags ::