Paul Robinson is pushing to secure a contract in January after six months as a free agent, report The Sun.
The former England international is 36-years-old and has been without a club since his release from Blackburn Rovers in the summer.
The goalkeeper has spent time working as a television pundit over the last few months, but The Sun claim he has been undergoing an intense training course to get fit recently, and has already spoken with more than one Championship clubs.
Current number one Marco Silvestri has had an up and down season, and at present the next man up as back-up is inexperienced teenager Bailey Peacock-Farrell.
The club signed Ross Turnbull in the summer, but he has been sidelined with a broken ankle, and Leeds were recently linked with signing West Brom stopper Anders Lindegaard on loan, with the Express and Star newspaper suggesting they would return in January with an offer.
Unlike Lindegaard, Robinson is a goalkeeper who knows the Championship, and will be particularly motivated to step in and play for Leeds if required.
His arrival could give everybody at the club a lift, and answer a position of need until the end of the season with barely any expense.