The former Leicester City, Blackburn and Derby star retired at the end of the 2010/11 season to concentrate on his work as a pundit on television and radio.
However, at the age of 37, Savage now says he is willing to help out the Rangers 'newco', set up after the former club was wound-up due to gross financial mismanagement.
"Rangers are struggling for players (and) I would come out of retirement and play for nothing…I could do a job in Scottish Division 3," the former Wales international wrote on Twitter.
"It would be a privilege to play for a great club ... I only retired a year ago.
"I might be mad thinking I can but if they're desperate for players, I’ll go up there and play for nothing!
"You think I’m joking, I’m serious. I’ve sent a text to (Rangers chief executive) Charles Green already to ask (manager) Ally (McCoist) if he needs any help! The offer is there we will wait and see."
Rangers are desperate to sign players before September 1st when a one-year transfer embargo begins at the club.
Former Hearts players Ian Black and Craig Beattie are already training with the club and Dean Shiels, Steven Jennings and Kevin Kyle have also been linked with moves.
However, Rangers cannot sign anybody until they are granted membership of the Scottish Football Association which they have not yet received despite being due to play Brechin in the Ramsden Cup this weekend.
Talks between the Scottish Premier League and Ibrox chief Green, which are crucial to the Ibrox club's bid to become part of the SFA, are ongoing.