Shorey has refused to sign a new contract with the Royals - and only has two years left to run on his current deal.
Royals boss Steve Coppell would be loathe to lose one of his key players - but wants to avoid a repeat of the situation which saw star midfielder Steve Sidwell join Chelsea on a free transfer this summer.
Hammers boss Alan Curbishley is in the market for a new left-back having sold Paul Konchesky to Fulham - and Irons chairman Eggert Magnusson is ready to stump up the cash for Shorey, according to the Sunday Mirror.
The 26-year-old feels a move to Upton Park will enhance his chances of securing a regular spot in Steve McClaren's England plans.
And it is unlikely the Hammers will have any trouble agreeing personal terms with the full-back if the Royals accept their bid.