The Reds’ rearguard ultimately cost them a first ever Premier League title last term after being breached on 50 occasions over the season, and the addition of Dejan Lovren over the summer has done little to address the issue since then.
A difficult opening seven games for the Merseysiders leaves them with a 0 goal difference, with defeats at the hands of Aston Villa and the Hammers a concern for Brendan Rodgers.
Reid has now emerged as a target to solve the issue, with the New Zealander having impressed for the Irons since their return to the top tier.
Manchester United are also keen on the 26-year-old, whose contract expires at the end of the season.
Although a key man for them, West Ham may opt to sell in the next transfer window, with the prospect of losing the commanding centre-back for free far from attractive.
The Kiwi found the back of the net in the Hammers’ 3-1 win against Liverpool this season.
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