Advocaat quits as Belgium coach
Belgian and Russian media have reported in recent weeks that the Dutchman was set to replace compatriot Guus Hiddink as coach of Russia.
The Belgian FA said in a brief statement that it would be seeking legal advice to determine what action to take.
Advocaat, 62, only took charge of the Belgium team at the start of October last year, with the goal of securing their qualification for Euro 2012.
Belgium, whose last appearance at a major championship was in the 2002 World Cup, had already missed out on a place in the finals in South Africa this year.
Advocaat, nicknamed the "Little General," arrived from Zenit St Petersburg, who he led to UEFA Cup triumph in 2008. He has previously coached the Netherlands, South Korea and United Arab Emirates.
Belgian media reported last year that the Dutchman had been keen to move to Belgium to be nearer to family and friends and that he would earn 600,000 euros a year, a figure the Russian football federation is likely to top.
Advocaat has also been coach of Dutch champions AZ Alkmaar since December.