The moves come after the TFF earlier this month suspended 149 referees and assistant referees after an investigation found that the officials working in the country's professional leagues were betting on football matches.
Turkey's state-owned Anadolu news agency said a court had ruled to arrest Eyupspor Chairman Murat Ozkaya and seven others as part of the investigation.
Eyupspor were not immediately available to comment.
In a statement, the TFF said it had sent 1,024 players from all leagues to the Professional Football Disciplinary Council (PFDK) as part of the investigation, including 27 players from the top-tier Super Lig, who have all been suspended.
Among those 27 were players from champions Galatasaray and Istanbul rivals Besiktas, among others.
"Due to the precautionary transfer of 1,024 football players to the PFDK, negotiations have been initiated urgently with FIFA to grant a 15-day transfer and registration period in addition to the 2025-2026 winter transfer period, only at the national level, in order for clubs to complete their squad deficiencies," the TFF said.
It also said matches in the second and third-tier leagues were suspended for two weeks, while local media said the TFF board would hold an extraordinary meeting at 1400 GMT on Tuesday.
Football's world governing body FIFA did not immediately respond to a Reuters request for comment on the probe and the TFF request for a 15-day transfer window.
TFF President Ibrahim Haciosmanoglu has described the situation as a "moral crisis in Turkish football".
Its own investigation revealed that 371 of 571 active referees in Turkey's professional leagues had betting accounts, and 152 of them were actively gambling.
One referee had bet 18,227 times and 42 referees had bet on more than 1,000 football matches each. Others were found to have bet only once.