The 29-year-old, who was capped by Bulgaria immediately after obtaining citizenship earlier this year, had agreed a three-year contract on Monday but the BFU has held up the transfer, claiming CSKA owed money to three local sides.
"The transfer is blocked as CSKA still owe 421,000 levs ($319,022) to Sliven," BFU vice-president Yordan Lechkov told local media on Wednesday. "They'll not be allowed to sell or buy players until the debts are settled."
Lechkov added that CSKA also owed money to Chernomorets Burgas and Slavia Sofia, without revealing the amounts.
CSKA, however, plan to appeal the decision in court.
"We're preparing a complaint to the Sofia prosecutor as we think the actions undertaken by the BFU are unlawful and lower the prestige of the club," the 31-times Bulgarian champions CSKA said in a statement.
The Cypriot club also expect the transfer to proceed but the delay will prevent them from using the midfielder as soon as they had hoped.
"We have a perfectly legitimate contract with Marquinhos and CSKA and we should be able to sign him in 30 days according to UEFA's rules," Anorthosis coach Stanimir Stoilov told Bulgarian media.
"But the delay will affect our plans as we wanted to use Marquinhos in the Europa League."
Anorthosis play Macedonia's Rabotnicki in the third qualifying round of the European competition over two legs on Thursday and August 4.
