England Under-21 defender Chambers is in talks with Crystal Palace over £16m deal.
Chambers impressed on a season’s loan with Middlesbrough last season and is seen by Palace as a cheaper option than £30m-rated Liverpool centre-half Mamadou Sakho.
Carl Jenkinson and fellow full-back Kieran Gibbs are also free to leave the Emirates this summer.
Jenkinson is attracting strong interest from Swansea and Brighton.
Gibbs, who is valued at £12m, is a target for Watford after West Brom pulled out of the running.
Arsene Wenger is looking to slash his numbers with injury-hit midfielder Jack Wilshere and out-of-favour Lucas Perez on their way out.
Wenger, who insists contract rebel Alexis Sanchez is staying put, still retains a strong interest in Monaco’s Thomas Lemar.