It was reported that Arsenal had an accepted a loan-offer for the wing-back from Galatasaray, with the player left debating the switch to Turkey.
However, the Hammers have now thrown their hat into the ring, and are keen on adding Debuchy, with star left-back Aaron Cresswell out for the first four months of the new season through injury.
The Gunners have their own injury concerns to worry about, and could delay any move involving Debuchy until some of their defenders return to full fitness. Per Mertesacker will be out until the new year, whilst Gabriel and Laurent Koscielny are doubts for their league opener against Liverpool.
West Ham are looking to build a squad capable of playing in both the Premier League and UEFA Europa League, after booking their place in the final qualifying rounds for the European competition.
The club will face Astra Giurgiu, who knocked them out of the qualifying stages of the competition last year.