Rayo finished eighth in the Primera Division last season which would have earned them a place in the Europa League due to sixth-place Malaga's exclusion, but were refused a UEFA licence by the Spanish Football Federation (RFEF) because of outstanding debts.
The Madrid-based club appealed to CAS to get both the RFEF's ruling overturned and also for provisional measures that could have enabled them to be included in next week's draw for the third qualifying round of the Europa League.
However, CAS on Thursday rejected the provisional application, while confirming a hearing to decide on the case's full merits is set to be held in the next few weeks.
A CAS statement read: "The Court of Arbitration for Sport has dismissed the application for provisional measures filed by the Spanish club Rayo Vallecano in relation to a decision of the Spanish FA (RFEF) refusing to grant the UEFA licence to Rayo Vallecano for the 2013/2014 season for the reason that the club had overdue payables when the attribution of UEFA licences had to be determined by the first instance of the RFEF licensing committee.
"Rayo Vallecano had filed both an appeal and an application for provisional measures requesting CAS to order RFEF to grant the UEFA license to Rayo Vallecano so that the club could participate in the 2013-2014 UEFA Europa League competition.
"The arbitration in this matter is ongoing and an award on the merits will be issued at the end of the CAS appeals procedure. A hearing is likely to be held within the next few weeks."
Malaga last month saw their appeal against a ban preventing them from playing in European competition this coming season dismissed by CAS.
In December, UEFA ruled Malaga would be ineligible to play in Europe for two years, later reduced to one, for violations of financial fair play rules.