The 34-year-old has not featured since the 1-1 draw with Elgin at Ibrox on January 5 and has suffered pain which has restricted his training.
He will now have a second scan on the problem and faces further time on the sidelines.
Manager Ally McCoist's squad is stretched and the manager revealed that Ross Perry and Francisco Sandaza are also unlikely to return to the team for Saturday's game away to Clyde.
He said: "Lee is struggling unfortunately. He has been having this pain in his ankle and we are going to send him back for another scan.
"Obviously the injury is not right and we need to get it right.
"Perry and Sandaza are also still struggling. Ross came off with a hamstring injury at Tannadice while Fran has a thigh muscle pull so we don't expect either of them to be fit for the weekend."
Striker Kevin Kyle is still doubtful and both Lewis Macleod and Darren Cole are out long-term while Kal Naismith serves the second of a two-match ban this weekend after his dismissal at Tannadice in the Scottish Cup on February 2.
Meanwhile, McCoist has confirmed his interest in recruiting Kilmarnock goalkeeper Cammy Bell for next season when the club's transfer embargo ends in September.
However, he has stressed that a deal has not been done and talks have yet to take place.
He told RangersTV: "We are interested in Cammy Bell. We would like to keep Neil Alexander as well because I want to have two strong goalkeepers and then it would give me the opportunity to send Scott Gallacher out on loan.
"Nothing has been finalised but he is a player we hope to have a chat with and find out what his situation is."
Meantime, Gers hope to secure youngster Fraser Aird on a new deal.
Toronto-born Aird, who has just turned 18, has only started five matches but scored a stoppage-time winner at Hampden from the bench against Queen's Park in December.
McCoist said: "It would be ideal if we could tie down Fraser on a long-term contract.
"We are looking to tie down our better younger players on longer deals and we have already managed to achieve that with Lewis Macleod, Barrie McKay and Robbie Crawford.
"Hopefully, Fraser will be another one we can look at and we can sit down with his representatives and we can get a contract agreed and signed and he can continue his progression."