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The Stoke City midfielder has played just three Championship games for the 14th-placed side this season.
Adam, 32, spent six years at Ibrox before moving to Blackpool in 2009 – and a reunion with former Liverpool team-mate and Rangers manager Steven Gerrard could be of interest in January.
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Someone asked me at the weekend if Id be interested in going back to Scotland to play and I need to play, Adam, who played with Gerrard at Anfield during the 2011/12 season, told talkSPORT.
If there are options there, well sit down and look at them, if theres not then Ill stay at Stoke and try to get an opportunity to play.
Adam is behind Etebo Oghenekaro, Ryan Woods and Joe Allen in the pecking order at the bet365 Stadium.
Predicted Rangers XI as Steven Gerrards men welcome Livingston
And a January move to Rangers could aid their title push – Gerrards men are just two points behind leaders Celtic.
Charlie Adam eyes up possible loan move out of Stoke City
Rangers winger Ryan Kent is “a couple of weeks” from fitness, while team-mate Borna Barisic is “very close” to a comeback, says manager Steven Gerrard.
Kent Back In Two Weeks
A hamstring injury has kept on-loan Liverpool winger Kent, 22, out since the win over St Mirren on 3 November.
Rangers return from the international break against Livingston in the Scottish Premiership on Saturday.
“The international break has come at a good time for Ryan,” Gerrard told the Rangers website. “He is probably now a couple of weeks away.
“Borna is very close; whether he is available for the weekend we will make a decision in the next couple of days.”