The English defender is a reported target of Fulham, who are promoted to the Premier League.
Chambers was on loan at Fulham two seasons ago.
Now the 25-year-old, who is back in training after a knee injury, could be on the move.
The Gunners want to secure more funds to complete the squad overhaul manager Mikel Arteta desires.
They are targeting a centre-half or two, a defensive midfielder and one or two wingers.