Etherington arrived from West Ham in 2009 and has gone on to make 177 appearances in all competitions for Stoke, including the 2011 FA Cup final and the subsequent UEFA Europa League campaign.
The 32-year-old only made 11 appearances under Mark Hughes this season, with only five of those starts, but is now a free agent after his contract was not renewed.
Goalkeeper Thomas Sorensen may extend his stay at the Premier League club after he was offered a new one-year contract.
The Dane, understudy to Asmir Begovic, has yet to agree to the deal that would extend his association with Stoke into a seventh year.
Hughes has already begun his recruitment for the new campaign with the signing of defender Phil Bardsley on a three-year contract from Sunderland.
