Kenya launched military action in Somalia last month after blaming the al-Shabab group for a spate of abductions on its territory.
Al-Shabab, which denies involvement in the abductions, has vowed to retaliate.
The 9,000-strong AU force is currently made up of Ugandan and Burundian soldiers, with Djibouti and Sierra Leone expected to bolster its numbers to 12,000 by the end of the year.
The African Union says it would like to increase its numbers to 20,000 but so far, there have not been enough concrete troop offers.
Al-Shabab, which is linked to al-Qaeda, controls most other parts of southern and central Somalia.
Kenya's President Mwai Kibaki discussed Kenya's offer with his Somali and Ugandan counterparts - Sheikh Sharif Ahmed and Yoweri Museveni respectively - in Nairobi on November 16.
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