Sporting Lisbon are asking to be compensated after Gelson Martin's move to Atletico Madrid earlier this week.
Atletico signed the winger on a six-year contract after taking advantage of chaos at Sporting, the Portugal international's former club.
The Cape Verde-born winger, who moved on a free transfer, succeeded in getting his release from Sporting after falling out with former president Bruno Carvalho last season and an attack by more than 50 fans at the training ground in May.
However, the 23-year-old's former club have accused Atletico of "unacceptable behaviour" in the deal and have asked FIFA to intervene.
"The board of directors of Sporting Clube de Portugal Futebol SAD decided unanimously to present ... FIFA with a compensation claim to the athlete and the club, and request ... sports sanctions to both," a statement on the club's website read.
Reports in the Portuguese media say Sporting are asking for compensation of between €60 million ($69.9m) and €100m.
Sporting have also complained to FIFA over Rui Patricio joining Premier League side Wolverhampton Wanderers as a free agent after the Portugal goalkeeper also cut ties with the club after the training ground incident.
Martins is expected to join Atletico's preseason training alongside others who were at the World Cup but did not make the final stages of the tournament, including Spain internationals Saul Niguez and Koke.
ESPN FC Spain correspondent Dermot Corrigan contributed to this report.