Piturca was entitled to EUR600,000 in compensations if dismissed, but, following talks with Federation officials, he agreed to resign.
According to sources, Piturca is likely to receive nearly EUR300,000 following his resignation.
Prominent football figures Razvan Lucescu, Cosmin Olaroiu and Gheorghe Hagi are among contenders for this position.
Earlier Thursday, Piturca said he does not want to have his contract with FRF terminated, stressing he had two options, either to resign or to be unilaterally dismissed.