Newly-promoted Fulham are believed to be interested in signing 23-year-old Chambers, but it looks as if they may have to wait for their man as, according to the Daily Star, Emery weighs up his options.
Despite showing a great deal of potential, Chambers has never really progressed at Arsenal, becoming very much a bit-part player at the north London club. He was previously loaned out to Middlesbrough in 2016, where he made 24 appearances as they were relegated back to the Championship.
Fellow defending Rob Holding only made 12 Premier League appearances last season, instead being used more often in the Gunners' Europa League campaign.
Greek international Sokratis Papastathopoulos is expected to complete a £16 million from Borussia Dortmund to Arsenal before the transfer window is out, meaning game time for the pair may become even more unlikely.
The understanding is that both Chambers and Holding want to remain at Arsenal and fight for their place in the side however, but if they don't perform, they might have no option but to leave north London.
Emery, however, has reportedly been less forgiving to Arsenal's other bit-part players. The London Evening Standard reports that forwards Joel Campbell and Lucas Perez are set for the axe, as the Gunners look to clear out some deadwood.
Neither Perez or Campbell have shown anything to suggest that they could be potential starters for The Gunners, with Campbell being farmed out on loan six times since joining the club in 2011. Perez meanwhile made just 11 appearances in his debut season, before he too was shipped out on loan.
The new Arsenal manager will be keen to put his mark on a side that has stagnated in recent years under Arsene Wenger. By getting rid of some of Arsenal's less valuable players, the rest of the squad may be injected with a more competitive spirit.