The Canaries star has already confirmed to talkSPORT he's leaving Carrow Road this summer.
That's despite him having another year left on his contract with the Championship outfit.
The Norwich academy graduate made 48 appearances in all competitions last season, scoring once and providing two assists.
Since becoming part of the Canaries' first team, Aarons has won promotion from the Championship twice during his 213 games for the club.
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He also already has 70 Premier League appearances under his belt.
Aarons attracted interest from Barcelona in 2020 summer, with the Canaries reportedly rejecting two big-money bids from the Spanish giants.
The Hammers were also keen on the defender in 2021, but a move never materialised.
Should he join West Ham, he'll boost the Hammers' options at right back alongside Vladimir Coufal and Ben Johnson.
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The east London outfit haven't signed anyone since they lifted the Europa Conference League trophy earlier this month.
However, they have agreed a deal worth £105million to sell Declan Rice to London rivals Arsenal and given their captain permission to have a medical.
talkSPORT understands Leicester star Harvey Barnes is also on West Ham's wishlist as they plot a transfer raid with the funds generated from Rice to Arsenal.