Armitage has written to President Chen Shui-bian, Premier Su Tseng-chang and Defence Minister Lee Jye asking that L-3 Communications be allowed to bid for the arms deal, the Chinese-language China Times said.
The planned purchase, which is struggling to gain parliament's approval, is part of the island's efforts to boost defence capabilities against rival China.
Taiwan's defence ministry has been inclined to reward Lockheed Martin with the contract worth about 40 billion Taiwan dollars (1.21 billion US), the newspaper said.
"Giving the contract to Lockheed Martin would be in the greatest interest of Taiwan as it is the original manufacturer and is rich in experiences ranging from depot maintenance to personnel training and upgrade of the aircraft," the paper quoted an unnamed military source as saying.
The 12 aircraft used by the US navy would be refurbished and upgraded before their delivery to Taiwan.
When asked to comment on the report, Premier Su said the deal would be handled in accordance with the law.
US President George W. Bush in 2001 offered the sale of six PAC-3 Patriot anti-missile systems, eight conventional submarines and 12 P-3C aircraft.
However, the mega arms deals have repeatedly been blocked by Taiwan's opposition-controlled parliament. The bill's latest version is worth around 340 billion Taiwan dollars (10 billion US).
Some opposition lawmakers say Taiwan cannot afford the arms deals while others say the submarines would be delivered too slowly to enable the island to keep pace with China's military build-up.
Military analysts said as the P-3C deal is the least controversial, it is expected to receive the nod from parliament within the next few months.
China regards Taiwan as part of its territory and has said it is prepared to use force if the island declares formal independence, prompting the island to secure more advanced weaponry from the United States. The two split in 1949 after a civil war.
L-3, whose clients include the US Department of Defence, is a merchant supplier of secure communications technology, training and simulation, avionics and other specialist products.

Copyright AFP (Agence France-Presse), 2006