The Hoops are scheduled to fly to Slovenia on Tuesday for Wednesday's first leg tie, and the Polish club are due to play in Kazakhstan the following night.
Uefa initially announced they were not prepared to be participate in a fast-track hearing by CAS.
But, last night, CAS agreed to Legia's request to proceed with a hearing on Monday, at which they claim they can decide to impose 'provisional measures.'
Legia are demanding this includes postponing next week's play-off ties involving themselves and Celtic until a full hearing can be arranged.
CAS have requested Uefa and Celtic provide written observations for consideration at Monday's hearing.
But, Uefa had already made it clear they intend to wait for a full hearing before they defend their decision to call a forfeit on the game which saw Legia field an ineligible player.
And Celtic have maintained from the outset this is a matter between Uefa and Legia.
Ludowik Zukowski, a lawyer who has represented several Polish athletes in CAS hearings, has warned Legia there is only a 1% chance of having the ties postponed.
Meanwhile, Derk Boerrigter has been cited for diving during Wednesday's win over St Johnstone.
He has been offered a two-game fixed penalty by the SFA.
He has until 3pm on Monday to appeal, and a hearing would be scheduled for Thursday.