Reid, 26, is out of contract at the end of this season, and doesn't appear set to sign a new deal to stay with the Hammers, with Liverpool allegedly eyeing a £6.5m move to sign the New Zealand international before Monday's transfer deadline.
West Ham already have a crisis at centre back, and losing Reid would mean manager Sam Allardyce would have to sign another defender at short notice - fortunately, he appears to have identified his contingency plan.
The Mirror suggest that former Tottenham defender Corluka, 28, is Allardyce's preferred choice should Reid leave before the end of the transfer window.
Croatian international Corluka, who is currently plying his trade in Russia with Lokomotiv Moscow, made 47 appearances for Manchester City before joining Spurs in 2008.
Corluka was a regular at right back for Tottenham, playing over 100 games for the club before a loan move to Bayer Leverkusen in 2012 and ultimately a permanent departure to Moscow just months later.
Now more of a centre back, Corluka could make a return to London as West Ham line up a move to bring him back to the capital as Reid's possible replacement.
The 6ft 4in centre back is a dominating presence in the air and could be a smart addition should Reid leave, and has plenty of experience behind him with 80 caps for Croatia.
Should Corluka arrive at Upton Park, he would follow in the footsteps of his former Croatia and Lokomotiv Moscow boss Slaven Bilic, who also used to play for West Ham - and the ex-Hammer could even persuade Corluka to make the move to East London should West Ham come calling in the next 48 hours.