Nigeria wants former oil minister extradited from Britain
Alison-Madueke, who served under president Goodluck Jonathan and was the first female head of OPEC, was arrested in London in October 2015 as part of an investigation into global corruption.
She has been on bail ever since, and been linked to a string of money laundering, bribery and asset recovery cases in Nigeria, Italy and the United States.
The former minister, 57, has always denied claims that billions of dollars were siphoned from oil deals and state accounts, including to pay for properties in exclusive areas of Lagos and London.
Nigeria's government has previously appeared happy to have Alison-Madueke potentially face trial in Britain.
A judge in Lagos in November last year even accused her of seeking to "avoid justice" after her lawyers applied to have her name attached to a fraud case.
Nigerian court cases frequently last years and there is criticism about corruption in the judiciary.
But the chairman of the Economic and Financial Crimes Commission (EFCC), Ibrahim Magu, said the British probe began even before he was appointed and she had still not been charged.
"It is very unreasonable that she is not being tried there," he told a news conference in the capital, Abuja.
"That's why I say, if you cannot prosecute her, bring her here. We will prosecute her... We cannot wait endlessly like this. I think three years and above is sufficient to take her to court."
He added: "There's no prosecution, nobody is prosecuting her there. That's why I said let us initiate (an) extradition process."
The Organisation for Economic Cooperation and Development (OECD) said in 2014 that the average length of time for investigations into foreign bribery was just over seven years.
The British investigation is being conducted by the National Crime Agency (NCA), which targets serious and organised criminal activity in Britain and around the world.
Any Nigerian application for extradition would be made to the interior ministry in London and require the approval of the interior minister.
Nigerian President Muhammadu Buhari was elected in 2015 on a promise to root out endemic corruption and end impunity in Africa's most populous nation.
That included reforming the notoriously opaque Nigerian National Petroleum Corporation (NNPC) which Alison-Madueke oversaw.
But three years on, and as he seeks re-election at polls in February next year, he has yet to secure a big-name conviction, after claims he has targeted political opponents.
Magu said the EFCC had secured 703 convictions since he took over in 2015, including two former state governors, in what he said was "an unprecedented fight against corruption".
Since November 2015, Magu said some $2.2 billion (1.96 billion euros) of "looted funds" had been recovered through court orders, as well as hundreds of properties from filling stations to hospitals.
JOIN OUR PULSE COMMUNITY!
Eyewitness? Submit your stories now via social or: