Taylor is accused by a UN-backed war crimes court in Sierra Leone of masterminding a policy of murder, torture, pillage and rape in Liberia and Sierra Leone, where prosecutors have lodged a 17-count indictment alleging crimes against humanity.
Kofi Annan's office issued a statement late on Tuesday, saying the UN chief "calls on all countries in the region not to give refuge to Mr Taylor, but to execute the warrant for his arrest".
The statement also urged those countries to comply with Liberian President Ellen Johnson Sirleaf's request that Taylor be transferred to the Special Court in Sierra Leone.
On Tuesday, Annan said that, if confirmed, Taylor's disappearance would be "extremely worrying".
Taylor had been living in exile in southeastern Nigeria until Monday night, when he was found to have left his luxury villa, only two days after Olusegun Obasanjo, the Nigerian president, said the government of Liberia "could take him into custody".
Annan said: "I have heard the news. We are trying to get more facts about it. It would be extremely worrying if indeed he had disappeared."
The UN secretary-general said he was trying to talk to Nigerian authorities about the case.
In August 2003, in a bid to bring an end to civil war, Obasanjo invited Taylor to step down as president, leave his besieged capital, Monrovia, and accept political asylum in Nigeria.