* Nikkei eyes 11th straight day of gains
* Oil highest since Sept as Iraq govt seizes Kurdish-held Kirkuk
* U.S. short-term rates soar on report Trump meets Taylor
TOKYO, Oct 17 (Reuters) - Oil prices held firm on Tuesday after Iraqi forces seized the oil-rich city of Kirkuk from largely autonomous Kurdish fighters while Asian shares look set to extend their bull run on optimism about upcoming earnings.
Short-term U.S. bond yields and interest rates jumped after a report U.S. President Donald Trump favoured Stanford economist John Taylor to head the Federal Reserve.
Japan's Nikkei gained 0.6 percent, extending its 10-day winning streak until Monday while MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.04 percent having gained 10 of the past 12 sessions.
Oil prices held near their highest levels in more than two weeks after Iraqi government forces captured the major Kurdish-held oil city of Kirkuk in a response to a Kurdish independence referendum, raising worries about oil supply.
As Iraqi forces advanced, Kurdish operators briefly shut some 350,000 barrels per day of oil output at two large Kirkuk fields, citing security concerns, oil ministry sources on both sides said.
Although production resumed shortly thereafter, concerns about supply disruptions and further escalations in the confrontation between Baghdad and the Kurds kept investors on edge.
U.S. crude traded at $51.85 a barrel, little changed on the day, after having hit a high of $52.37 on Monday. Brent crude fetched $57.85 per barrel, having risen to as high as $58.47 on Monday.
U.S. short-term interest rates and bond yields jumped on Monday after Trump met Stanford University economist John Taylor to discuss the job of Federal Reserve Chair as Trump seeks candidates to succeed current Janet Yellen next year.
Taylor is known as a proponent of a rule-based monetary policy and according to his formula, known as Taylor rule, the Fed funds rate needs to be much higher than the current target of 1.0 - 1.25 percent.
The policy-sensitive two-year yield jumped to as high as 1.546 percent, its highest since 2008, while Fed funds rates futures contract for settlement in late 2018 to early 2019 posted one of their biggest fall so far this year.
Trump has met other candidates, including former Fed Governor Kevin Warsh, current Governor Jerome Powell and he will see Yellen on Thursday, leaving markets on tenterhook.
"At the moment, there's no consensus at all in the market and there is little point betting on who will be picked as it would be a complete gamble. But once the decision will be made, there will be a clearer market direction," said Tomoaki Shishido, fixed income analyst at Nomura Securities.
"And when the uncertainty is cleared, bond yields are likely to rise given the strength of the economy now," he added.
Major currencies are also largely on hold.
The euro traded at $1.1792, little changed from the previous day.
The dollar bounced back to 112.16 yen, from Monday's low of 111.65, which was its lowest since Sept 26.
Elsewhere, copper soared to $7,134.5 a tonne, hitting a three-year high, having jumped 3.7 percent on Monday, its biggest gain in about 10 months.
(Editing by Sam Holmes)