Johnson, 30, came up through the West Ham academy but left the club in 2003, joining Chelsea before spells with Portsmouth and Liverpool.
The former England international racked up 200 appearances for the Reds, but was released this summer upon the expiration of his contract at Anfield, meaning he is now a free agent.
The Sun believe that Johnson has not only snubbed a move to Turkey with Besiktas, but wanted a move back to Upton Park this summer.
However, the Hammers are more likely to pursue another deal for Arsenal's Carl Jenkinson, who impressed for West Ham during a year-long loan deal last season.
That leaves Johnson without a club, and seemingly little interest from clubs in England right now, who saw Johnson struggle last term.
Johnson - a good option for West Ham?
New Hammers boss Slaven Bilic will be keen to tie Jenkinson down to another loan deal at Upton Park, with the 23-year-old starring last season.
Yet, if they can't secure that deal with Arsenal, West Ham will need other targets in mind - and Johnson could be an interesting alternative.
He may be seven years old than Johnson but he would seemingly have the desire to play for West Ham again, and whilst his defensive issues have been highlighted over the years, he could still have something left in the tank. On a free transfer, West Ham could do worse; but only if they miss out on Jenkinson.