Sion today revealed they had launched an appeal to UEFA, although the European governing body have yet to receive it.
Constantin has vowed to take his team to Madrid for the Europa League group opener against Atletico next Thursday despite Celtic being reinstated in the competition at their expense.
Protests from Celtic over Sion playing illegible players in the Swiss side's 3-1 aggregate were upheld on Friday, but uncertainty remains over who, if anyone, will face Atletico on September 15.
In a statement issued to Press Association Sport, a Sion spokesman said: "FC Sion yesterday received 12 pages of confused explanations (in French) for the acceptance of the protest.
"The decision comes from the three UEFA judges who decided to keep Celtic in the competition. For us, it's a pure revenge against our president.
"FC Sion officially appealed to UEFA on Monday, in order to obtain the cancellation of the protest.
"We remind that Celtic received before its home game an official document from the European federation: it mentioned that players were officially eligible.
"Sion prepares its travel to Madrid.
"Players (individually) and the club are now bringing legal actions against UEFA at Swiss civil court.
"Civil court already gave the players the right to play (before the games), that was not respected by the UEFA. "This is a serious violation of Swiss laws and may result in penal proceedings."
A UEFA spokesman this morning told Press Association Sport they had not yet received anything from Sion, but the Swiss club also announced they had made an appeal in a brief statement on their official website.
Sion were handed a transfer embargo for breaching rules over the signing of Egypt goalkeeper Essam El-Hadary three years ago but the club and FIFA have different interpretations over the length of the ban.
Sion have already won a civil court ruling over the issue, which prompted their domestic football authorities to allow them to field the five affected players.
And the club are adamant UEFA gave them the green light to play them.
The players include former Hearts defender Jose Goncalves and midfielder Pascal Feindouno, who scored two goals as Sion beat Celtic 3-1 in Switzerland following a goalless first leg.
Celtic played both legs under protest and officially complained to UEFA after their defeat.
Sion were also drawn against Udinese and Rennes in Group I before being removed from the competition.
They have the right to challenge the decision in the Lausanne-based Court of Arbitration for Sport should their UEFA appeal fail.