"Elche CF are up to date with their tax obligations," the club said on their website (www.elchecf.es) on Friday.
The club, who have been provisionally replaced in the top flight by Eibar, added that they plan to file the appeal with the government disciplinary committee for sports (TAD) on Tuesday along with a certificate from the tax agency.
Elche, who finished 13th last season, were punished by La Liga for "very serious infractions" of Spain's sports law and league rules and were fined more than 180,000 euros ($204,102).
Based near Alicante in south east Spain, the club owed around four million euros in unpaid taxes, local media have reported.
Asked later on Friday about Elche's statement, La Liga president Javier Tebas suggested the appeal had little chance of success.
"The Elche case is a closed case," Tebas told reporters after his organisation's general assembly in Villarreal.
"The fact they have resolved their problems with the tax agency will not change La Liga's decision."
Basque side Eibar featured in the top flight for the first time last season but were relegated on the final day after finishing 18th.
(Reporting by Iain Rogers, editing by Tony Jimenez)
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