The England international has just spent a season on loan at Middlesbrough, where he made 26 appearances in all competitions.
However, now he has returned to the Emirates Stadium, his future looks uncertain with Gunners boss Arsene Wenger looking to make major additions during the summer.
According to the Daily Mail, Everton could look to the 22-year-old if they are unsuccessful in luring Burnley defender Michael Keane to Goodison Park.
Should they push forward with their initial interest, Chambers could cost in the region of £15m as Arsenal look to recoup much of of the fee they paid Southampton in 2014.
The versatile defender has made a total of 59 appearances for the North London outfit in all competitions.