Jamal Ibrahim, a foreign ministry spokesman, said on Sunday: "This is a final decision. We are asking them to leave since they indicated that they will not be able to continue their mission."
An AU spokesman said it had not been informed officially of any such decision and declined to comment.
Khartoum rejected a UN Security Council resolution that was passed on Thursday to deploy more than 20,000 UN troops and police to its remote west, after AU troops were not able to stem violence in the region.
Ibrahim said Sudan resented AU declarations that it supported a UN transition.
"We feel that they have no right to transfer their assignment to another party - we are the ones who decide whether we continue with the AU or not."
He said the government would implement its plan for Darfur, submitted to the Security Council, which includes sending 10,500 government troops to the region.
Rebels who did not sign the deal say those troops have already deployed and have begun attacking civilians and their positions in North Darfur.
The AU has confirmed that an offensive began last week ahead of the resolution.
Tens of thousands have been killed and 2.5 million forced from their homes since mostly non-Arab rebels took up arms against the Arab-dominated government in early 2003, accusing the central government of neglect.
The international criminal court is investigating alleged war crimes in the region.
Washington calls the violence 'genocide', a charge Khartoum rejects.