"I have pressed charges and will consult with my lawyer about the next steps," he told German sports news agency SID, according to daily Bild.
The 64-year-old coach said he would still attend his team's Euro 2012 qualifying match against Germany on Tuesday night, out of "love for the association."
Vogts came under heated criticism from local media after Azerbaijan's 1-2 loss to Kazakhstan in Friday's qualifying game.
He has been rumoured as a possible successor to Guus Hiddink, coach of Turkey's national team. Meanwhile, the president of Azerbaijan's football league, Rovnag Abdullayev, is also keen to keep Vogts once his contract expires in November, Bild said.