Sion were planning to launch a compensation claim against Uefa yesterday following their expulsion from the Europa League.
The Swiss club say they will make an initial claim of more than €4 million (Dh20.1m), with reports in the Swiss press suggesting the final demand could be for tens of millions.
Sion have also threatened to make a criminal complaint against Uefa after claiming a Swiss court backed their fight to be reinstated in the competition.
They were expelled from the tournament on September 2 for fielding ineligible players and saw their appeal rejected by Uefa's appeals body yesterday.
Glasgow Celtic, who lost 3-1 on aggregate to Sion in the play-offs, were handed their opponents' place in the group stages and travelled to Spain yesterday for their opening match against Atletico Madrid tonight.
A Sion spokesman said in an email: "We send today a first order to pay to Uefa , and directly to its president Michel Platini, for more than €4m.
"Uefa believes that it rules the world. The law of the jungle couldn't rule football."
The spokesman said: "Yesterday, it was a clear case of misfeasance. Swiss Court won't let the case fall, because they obliged Uefa to reintegrate immediately Sion … Uefa now infringes Swiss laws, that means that penal proceedings can be prosecuted."
Sion have now scrapped plans to travel to Madrid, despite Christian Constantin, the club president, previously claiming his side would make the trip regardless of the Uefa ruling.
However, they believe they could still be reinstated at a later date and plan to take their case to the Court of Arbitration for Sport.
Constantin told Swiss newspaper Le Matin: "What Uefa have done is to ignore the law of a state and its institutions.
"By violating the decision of a judge, those responsible have aggravated their case. For these gentlemen, the real trouble is going to start now."