Moyes is seeking to strengthen his West Ham side this month as they prepare for a fight to stay in the top-flight.
Moyes has identified Barkley as a prime target this month and hopes to land him on loan, according to The Mirror.
The pair previously worked together at Everton where Moyes spent 11 years as manager.
Barkley came through the ranks at the Merseyside club, playing his way up the youth sides until Moyes gave him his professional debut in 2010.
The Englishman was always a key cog in the Scottish manager's side until the latter took over at Manchester United in 2013.
Despite West Ham's eagerness to bring Barkley to the London Stadium, Chelsea are so far believed to be adamant that they wish to keep the player.
Frank Lampard has only used Barkley in seven of the Premier League matches so far, but that's partly down to an injury that kept him out for over a month.
Recently, however, Barkley has started in the games against Nottingham Forest in the FA Cup and at home against Burnley in the Premier League.
It must be noted that Lampard has normally relied more on the likes of Matteo Kovacic, Jorginho, N'Golo Kante and Mason Mount.
With Euro 2020 looming in the summer, Barkley will no doubt be keen to play as much football as possible to try and force his way into the England squad.
Moyes is reported to believe this may play into West Ham's favour, as he feels they can offer the 26-year-old more guaranteed game time.
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