Although Nigeria said it was ready to hand Charles Taylor over on Saturday, the tribunal fears that the exiled former president may flee to avoid standing trial for crimes against humanity.
Liberia's information minister, Johnny McClain, said on Sunday his government was working with other countries to get Taylor sent directly to Sierra Leone.
Taylor, who could not be reached for comment, is accused of starting a 14-year civil war in his homeland, brutalising tens of thousands of boys and girls drafted as rebel fighters.
He is also blamed for a war in neighbouring Sierra Leone where rebels - including child fighters - terrorised victims by chopping off arms, legs, ears and lips.
An international tribunal indictment says Taylor is responsible for the destruction of Liberia and Sierra Leone and for the murder, rape, maiming and mutilation of more than 500,000 Sierra Leoneans.
Each of the 17 charges he faces carries a sentence of life in prison.
Taylor also is accused of harbouring al-Qaida suicide bombers who attacked US embassies in Kenya and Tanzania in 1998.
"The watching world will wish to see Taylor held in Nigerian detention to avoid the possibility of him using his wealth and associates to slip away, with grave consequences to the stability of the region," the prosecutor of Sierra Leone's war tribunal, Desmond de Silva, said on Sunday.
"Certainly African leaders, members of the good old boy network, are under notice that you cannot destroy your own citizens for your own personal gain"
David M Crane, prosecutor
De Silva said he had sent a message asking Olusegun Obasanjo, the Nigerian president, to arrest Taylor.
The former Liberian leader has been in exile in the southern Nigerian city of Calabar since being forced from power in 2003 as part of an accord that ended a rebel assault on Liberia's capital.
Nigeria "has resisted persistent pressures to violate the understanding of 2003, giving Taylor refuge under an internationally brokered peace deal", Obasanjo said in a statement on Saturday.
Nevertheless, he had informed Liberia's president that "the government of Liberia is free to take former President Charles Taylor into its custody".
Taylor is accused of starting a
14-year war in his homeland
After her inauguration in January, Ellen Johnson Sirleaf, Liberia's president, said a trial for Taylor was not a priority. But she made a formal request to Nigeria after an official visit to Washington, which is the source of aid much needed to rebuild Liberia.
A Nigerian presidential spokesman denied in a statement published in ThisDay newspaper that Nigeria was reacting to pressure from the United States, where Obasanjo is traveling this week and is scheduled to meet the US president on Wednesday.
David Crane, the American prosecutor who drew up Taylor's indictment, said his extradition would send a powerful message.
"Certainly African leaders, members of the good old boy network, are under notice that you cannot destroy your own citizens for your own personal gain and you don't go after women and children - don't rape women, don't turn children into monsters," he said.
The indictment also alleges that Taylor was a pawn in a bigger plot drawn up by Moammar al-Gaddafi, the Libyan leader indicted as a co-conspirator, to take over several African nations over 10 years. It says Taylor and other African rebels were trained, armed and equipped by Libyan special forces.
The case is full of implications for African presidents, who include coup leaders and others accused of human rights violations. It could set a precedent for those living in comfortable exile as well as sitting leaders, such as those in the Sudanese government that the US accuses of genocide in the Darfur region.