The midfield superstar, signed on loan from Juventus on transfer deadline day, made his first appearance for the defending champions as a substitute in the 5-0 win over Hearts at Ibrox on Sunday.
His debut cameo raised hopes of a possible first start against Hibs in midweek but Rangers boss Giovanni van Bronckhorst has poured cold water on those suggestions.
“Ramsey is not quite ready to start yet,” he confirmed. “You can see his quality in training and in his early minutes. He is improving every day and it is great to see the improvements in only a week.”
Van Bronckhorst also revealed that defender Filip Helander, who has been missing since September with a knee injury, could return to face Annan in the Scottish Cup on Saturday.
He added: “Helander is really close to start getting minutes again. Hopefully, we can get him involved at the weekend.”