Legia Warsaw's pursuit of a Champions League reprieve at the Court of Arbitration for Sport (Cas) could reach a verdict as early as Monday.
Uefa rejected Legia's appeal against the punishment that led to Celtic's reinstatement in the competition.
The fielding of a suspended player against Celtic cost Legia their place.
But a Cas fast-track appeal process can be instigated to deliver a ruling before Celtic play NK Maribor in the play-off round.
However, all parties in the case need to agree to the decision being made at short notice.
The first leg of Celtic's tie is scheduled for Wednesday, while Legia Warsaw, who have been consigned to the Europa League, are due to face Aktobe in Khazakstan on Thursday.
The Polish club believed that Bartosz Bereszynski had served a three-game ban, only to discover that by not registering the midfielder for the previous round against St Patrick's Athletic his suspension still stood for the second-leg defeat of Celtic.
Legia Warsaw manager Henning Berg
Henning Berg guided Legia to two wins over Celtic but, as things stand, his side is in the Europa League
Uefa's disciplinary sanction for fielding a suspended player is for the match to be forfeited 3-0, a result which saw Celtic progress to the next round on away goals, having lost the first leg in Poland 4-1.
Now Legia must submit their case in writing by close of business on Friday if Cas is to hear the case on Monday.
"Cas can either render a decision on request for provisional measures (if requested by Legia) or organise an expedited procedure (with the agreement of Uefa) with a hearing on Monday and a decision on the same day," a spokesman for Cas said.
"The appeal shall be in writing; the other steps of the procedure can be determined by agreement between Legia and Uefa (hearing or no hearing, procedural calendar, etc)."
A provisional measure could be reached if all sides do not agree to the fast-track appeal procedure. In those circumstances, Cas would rule on the validity of Legia's case, essentially providing the club with a verdict before proceeding to the full appeals procedure.
Uefa would have to abide by Cas's decision, and so could reinstate Legia to the Champions League if the court found in the Polish club's favour.
A ruling in Uefa's favour would leave Legia with only the Swiss courts as a final recourse.