"We know what he can do and he's an established Championship player," assistant manager Keith Millen told BBC Radio Bristol.
"And it does give us competition on the left hand side."
Millen continued: "It's a short-term contract and hopefully Tom and his agent will accept.
"We're still looking and if something comes up that we felt would improve the squad then we will do it.
"Tom, if you like, has got the shirt and it's up to him to show what he can do."
Williams, 30, started his professional career at West Ham and has also played internationally for Cyprus.
Source: BBC Sport
Source: BBC Sport