The Scottish Premier League has no immediate plans to reschedule Rangers' postponed ties at St Mirren and Celtic.
Rangers' fixture backlog is growing after the Scottish Cup fourth-round tie against East Stirlingshire was postponed due to a waterlogged pitch.
The cup tie will now be played on 23 January, meaning the Old Firm game will have to be moved for a second time.
Walter Smith's side have only one free midweek before March due to league and Uefa Cup commitments.
A statement from the SPL read: "Revised dates for the St Mirren v Rangers and Celtic v Rangers matches will not be announced before the end of the month."
Torrential rainfall led to Sunday's match at Ibrox being postponed.
Celtic were due to host Rangers on 2 January, but the game was postponed as a mark of respect for the late Motherwell captain Phil O'Donnell.
Rangers' league game against St Mirren last Tuesday was called off due to a waterlogged pitch.
"Rangers and Celtic are both heavily involved in a number of competitions - it's challenging to fit everything in"
"Obviously there is serious fixture congestion involving Rangers at the moment," said SPL Iain Blair secretary
"Rangers and Celtic are both heavily involved in a number of competitions. It's quite challenging to fit everything in."
The Ibrox club face Gretna at Fir Park on 16 January, before a trip to face Inverness on 20 January, then a home match against St Mirren on 26 January and a CIS Cup semi-final against Hearts on the 30th.
Rangers are due to face Celtic at Ibrox on SPL duty on 29 March and it is unclear whether there will be two Old Firm games in quick succession.
The Ibrox club said: "Free midweeks are few and far between due to the club's European commitments."
A statement on Celtic's official website read: "Celtic is naturally disappointed that the game with Rangers has been called off and sympathises with supporters over this postponement, which is obviously due to circumstances outwith the club's control."
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