The 46-year-old actor has been campaigning for an end to the conflict in the Darfur region of Sudan, and for humanitarian aid for the millions caught up in the conflict.
Nigeria's Movement for the Emancipation of the Niger Delta (MEND) congratulated Clooney on his appointment, and invited him to visit their impoverished region wracked by two years of fighting, bombings and kidnapping of foreign workers.
"Mr. Clooney, MEND extends an invitation to you to see things for yourself and is willing to work with you and other credible peace makers of international repute to stop Nigeria from plunging into the abyss of war," the group said in a statement.
The statement also said that the unrest in the region was building up to a crisis that could become worse than Darfur.
Clooney was not immediately available for comment.
The group asked for the UN to take an unspecified role in the conflict.
"We suggest that the U.N. should take a proactive step to nip the Niger Delta unrest in the bud before it is too late. Your role as a Messenger of Peace makes it imperative to consider the Niger Delta as a potential time bomb waiting to explode for which urgent steps must be taken."
The call for foreign interventon is unusual, as the group has so far used Africa's biggest oil industry as a leverage point to pressure Nigeria's government to meet its demands.
The demands include more oil revenue for the region, and the release from prison of some of the group's top leaders.
Attacks since early 2006 have cut Nigeria's oil production by about one quarter, aiding in the rise of oil prices.
Nearly 200 foreign workers have been kidnapped in the region in the past two years, with the hostages normally released unharmed after a ransom is paid.