The former Wales international last month offered to come out of retirement and play for Ally McCoist's side for nothing in the Irn-Bru Third Division.
The 37-year-old, who now works as a pundit, had claimed on his social networking page that the offer was genuine and that he had been in touch with Ibrox chief executive Charles Green.
However, Savage conceded on Tuesday morning that the dramatic move is unlikely to happen, although he stressed that his offer still stands.
He tweeted: "Just a quick update on rangers the offer is there and it will remain all season ally has my number and knows if he needs me I'll be there !
"But it's not going to happen at this moment, they have a good squad for div 3, and don't need an old codger like me ! Lol".
