Williams has been out of favour at Victoria Park following the emergence of youngster Jim Provett in Neale Cooper's first-team squad this season, having had a previous loan spell at Swansea City this term.
Hatters boss Sammy McIlroy has been keen to add goalkeeping cover at Edgeley Park since the departure of Nick Colgan back to Scottish Premier League side Hibernian.
He will act as cover for Stockport number one James Spencer but will hope to aid the club in their quest to pull away from the Division Two relegation zone.
