Nigeria's anti-graft agency has given 15 ex-governors wanted for corruption until the end of Friday to turn themselves in or face arrest.
Five of the former governors have already been quizzed by the Economic and Financial Crimes Commission (EFCC), an official has told the BBC.
EFCC chairman Nuhu Ribadu declined to name the ex-governors being probed.
The governors enjoyed immunity from prosecution until their terms of office expired last month.
The EFCC has said it was investigating almost all of the 36 governors on allegations of corruption.
Under Nigeria's federal system, governors wield considerable powers and some control budgets of more than $1bn a year in Africa's biggest oil producer.
"When the deadline lapses, we will declare them wanted according to our laws. We will obtain warrants and arrest them wherever they are found," Mr Ribadu told the BBC.
On the run
Some of the former governors have already fled the country, but Mr Ribadu says the EFCC will work towards having them extradited to answer graft and money laundering charges.
"They used to have constitutional immunity. Now they no longer have that. We have invited them to come, but if they don't, then we may have to take tougher steps.
"We shall declare them wanted and try to have them extradited from wherever they have fled to or have them tried wherever they have gone to."
Former Plateau State Governor Joshua Dariye has been questioned in the UK on money-laundering charges but skipped bail. His present whereabouts are not known.
Six governors were re-elected in April's elections and so retain their immunity.
Another seven won seats in Nigeria's Senate, even though one of them appears to have abandoned his seat and has reportedly fled to Spain.
But unlike the governors, parliamentarians are not protected from criminal prosecution under Nigerian law.
Nigeria is seen as one of the world's most corrupt countries.
New President Umaru Yar'Adua has promised to continue with his predecessor's campaign against corruption.
Critics of former President Olusegun Obasanjo say it was a cover to persecute his political rivals.
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