Burke, 20, is no stranger to Phil Parkinson, having played for Wanderers' manager whilst the pair were at Bradford City.
The England U20 international spent the 2015/2016 season on loan at Valley Parade, playing 36 games in all competitions, scoring two goals. For his efforts, Burke was crowned Bradford's Player of the Year.
Burke spent last season on loan with Wigan Athletic, but only managed to play ten games, scoring once. Burke is highly rated at West Ham, with some Hammers fans hoping the young centre back would be given a chance in the first team.
The youngster has played 12 times for West Ham, including a few appearances in the Europa League.
It's been reported in recent weeks that Wanderers have missed out on other centre back targets, with Raphael Branco and Nick Kuipers opting for moves to Portugal and The Netherlands respectively.
Would Reece Burke be a welcome addition to Wanderers' squad? Let us know in the comments box below.