The Gunners are being linked with a surprise move for the Brazilian playmaker, despite his poor showing in the Premier League last season.
The 27-year-old winger was unable to recreate the form he showed after moving to the London Stadium from Lazio in 2018.
West Ham paid an then club record £36million for the Brazilian and he did not disappoint, scoring ten goals and notching five assists in his first season.
But Anderson’s performance level dipped last term amid the sacking of Manuel Pellegrini, while West Ham struggled at the wrong end of the table.
According to The Mirror though, Arteta is understood to be a fan of Anderson based on his first season with the Hammers.
And the Gunners could be lining up a cut-price bid to try and tempt their London rivals into selling.
Should Moyes choose to sacrifice the wide man as part of his rebuilding plans, it would still leave the Scot with plenty of attacking options to support striker Sebastien Haller.
Andriy Yarmalenko, Michail Antonio, Roberto Snodgrass, Jarrod Bowen and Manuel Lanzini, can all operate behind the striker.
Anderson's value remains high despite his lack of form last season, but it would remain to be seen how much Arsenal would be willing to pay.
West Ham will want to recoup the initial £36m they paid for the winger but whether interested parties would want to pay that much is another story.
Anderson is also said to be keen on a new challenge and a return to Lazio appears to be one possible destination.
Should Arsenal sign him he would become the third Brazilian to join the club in a matter of weeks.
After Willian put pen to paper after leaving Chelsea, defender Gabriel Magalhaes was signed from Lille earlier this week.
And with David Luiz already plying his trade at the Emirates it could be quite the celebration of players from the South American nation.