A Swiss court has rejected an attempt by Sion to force Uefa to allow them to play Rennes instead of Celtic in Thursday's Europa League Group I game.
But Uefa president Michel Platini will appear before a Swiss judge on Wednesday to explain why it has not reinstated Sion to the competition.
European football's governing body has ignored an injunction won by Sion that they should be allowed back in.
Uefa wants the case resolved by the Court of Arbitration for Sport.
But that has been rejected by Sion, with a club spokesman telling BBC Scotland that they are concerned Cas is not sufficiently independent of Uefa to handle the case.
Sion were expelled from the tournament
after Uefa ruled that the Swiss club had fielded ineligible players during their 3-1 aggregate win over Celtic.
After losing an appeal to Uefa against the decision
, they defied world and European football rules that ban clubs from taking their cases outside sporting tribunals and won an injunction in their favour at a Swiss court.
But, despite being ordered to pay 1,000 Swiss francs for each day that the court order is not carried out, Uefa has argued that its own statutes prevent it from overturning a decision made by its independent disciplinary tribunal.
“The four clubs clearly stated that any change to the current Group I would impact on them significantly and therefore they have requested to be parties in the case”
It has instead asked Cas to consider the case and now Celtic, Udinese, Atletico Madrid and Rennes have all demanded to be part of the arbitration process by the Lausanne-based body.
The move comes after Uefa outlined plans to have Sion reinstated should they successfully pursue the case via Cas, although European football's governing body remains determined that the Swiss should be excluded.
Options offered by Uefa included cancelling all previous results in the group, putting Sion into the current group, or allowing them passage into the last 32 through a play-off.
"The four clubs clearly stated that any change to the current Group I would impact on them significantly and therefore they have requested to be parties in the case," said the latest Uefa statement in response to the Tribunal Cantonal de Vaud decision to deny Sion an injunction against this week's game.
"Uefa has already organised a meeting with the four clubs involved on Friday to discuss the various scenarios for the reintegration of FC Sion into the group should FC Sion win the case on the merits at the Cas.
"Uefa appreciates that any changes in the format of the Uefa Europa League need to be discussed with the four other clubs in the group that are affected by the matter."
Sion signed six new players in the summer despite a transfer ban imposed by Fifa.
However, a local Swiss court ruled that the ban no longer applied, leading to Wednesday's appearance by Platini, along with general secretary Gianni Infantino.
"Udinese Calcio, Celtic FC, Club Atletico de Madrid, Stade Rennais FC and Uefa have all urged the Cas to decide the case quickly," said Uefa.
"By contrast, it seems only FC Sion are still attempting to obstruct justice and delay matters in a way the Cas itself has described as "manifestly abusive".
"These clubs (like every other club in the competition with the apparent exception of FC Sion) all recognise the Cas as the sole authority competent to decide on the merits of the case and, as such, will respect whatever decision the CAS ultimately delivers."
Uefa insists that Celtic, who have already played games against
, will not be removed from the Europa League, even if Sion return.