The 33-year-old has made 54 appearances for England during his career, appearing at both the 2010 and 2014 World Cup's, but suffered heartbreak last season as Stoke were relegated from the top flight.
According to Football.london, Palace boss Roy Hodgson is looking to increase squad depth in the full-back position, making the out-of-contract Johnson an ideal signing for the Eagles. Hodgson is said to be looking for extra defensive experience, as he bids to avoid a repeat of last season's appalling start to the campaign.
The ex-Liverpool defender can play in a variety of positions, most notably in the full-back positions, and provides attacking options on the overlap, along with a strong defensive ability.
He made 64 appearances for Stoke in a three-year spell, but was restricted to just nine first-team appearances last season. In his heyday, Johnson represented both Chelsea and Liverpool, after graduating from the famed West Ham academy.
Johnson is not the only player to have been released by new manager Gary Rowett since his arrival at the bet365 stadium this summer, with veteran midfielder Stephen Ireland also made available to talk to other clubs at the expiry of his contract.
Crystal Palace meanwhile are also reportedly interested in Marseille right back Hiroki Sakai, who is rated around £12 million. The Eagles were keen on Fulham defender Ryan Fredericks too, but he has since signed for Premier League rivals West Ham.