Stoke are yet to address the issue of Victor Moses' future, with the winger having made a bright start to a loan spell.
Millwall boss Ian Holloway is ready to loan out some fringe players to free up room in his squad for some fresh faces.
Routledge has yet to sign the deal, but a Swansea spokesman confirmed to Press Association Sport the formalities will soon be completed.
The new contract will see Routledge remain with the Swans until the summer of 2016, and is reward for his excellent form since Michael Laudrup took over as manager in the summer.
The 28-year-old found first-team opportunities hard to come by during his first season at the Liberty Stadium, as then-manager Brendan Rodgers put his faith in Nathan Dyer and Scott Sinclair.
But the former Aston Villa, QPR and Newcastle wide man has been a regular starter this term, scoring five goals and revelling in the freedom he has been afforded by Laudrup.
Routledge would have been out of contract at the end of next season, having initially joined on a three-year deal from the Magpies in 2011, but is set to become the latest player to commit his future to Swansea.
Top scorer Michu, Michel Vorm, Ashley Williams, Neil Taylor and Ben Davies have all put pen to paper on new deals at the Liberty Stadium in recent months.