The Swiss club had brought a case against UEFA in Valais district court, which has now ruled the proceedings are "inadmissible".
Sion were kicked out of the competition after Celtic complained about the club fielding players signed while they were subject to a transfer ban.
A statement from the Valais court said: "According to applicable law, the dispute does not have sufficiently close links with the canton of Valais to have a basis of jurisdiction with the local judicial authorities Valais.
"The measures sought by the applicant were exclusively against UEFA, who have headquarters in Nyon."
Sion have until 11pm on Thursday to appeal against UEFA's decision to award Celtic the place in the Europa League group stage.