Savage offered to come out of retirement last month in order to help the Scottish club out of their crisis but has posted on Twitter that the move is now unlikely.
"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!" he tweeted.
"[However] 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!."
Assistant manager Kenny McDowall recently claimed that players must decide their future at the club soon.