By Phil Stewart and David Alexander

WASHINGTON (Reuters) - Defense Secretary Robert Gates could travel to China this year, the Pentagon said Thursday, following signs from Beijing of a willingness to resume military ties suspended over an arms sale to Taiwan.

China froze military-to-military contacts with the United States after the Obama administration in January notified Congress of a potential $6.4 billion arms package for Taiwan. Beijing then took the extraordinary step of turning down a proposed fence-mending trip by Gates in June.

"The Chinese have clearly signaled their interest in resuming military-to-military discussions, and we are right now exploring how best to do that," said Pentagon Press Secretary Geoff Morrell.

China's President Hu Jintao is likely to visit the United States next year, and Morrell noted that Hu and U.S. President Barack Obama have wanted the two militaries to engage more closely to avoid misunderstandings.

"We have not been meeting the mandate set forth by our respective presidents. So we do look forward to resuming military-to-military communication, exchanges, discussions with the Chinese," Morrell said.

Asked whether Gates might be amenable to traveling to China before the end of the year, Morrell said: "Sure." He cautioned, however, that the end of the year was fast approaching and there was little free time on the defense secretary's schedule.

"There was an invitation from the secretary's (Chinese) counterpart for him to travel there. It was then, I guess, retracted," Morrell told reporters at the Pentagon.

"So if it is being extended again, as it appears to be, we're going to certainly look for the possibility of trying to schedule that before the end of the year."

Throughout 2010, ties between Washington and Beijing have been tested over U.S. arms sales to Taiwan, Internet policy, Tibet, China's currency and Chinese territorial claims in the South China Sea. The gaping U.S. trade deficit with China, worth $226.9 billion in 2009, has fueled trade disputes.

U.S.-South Korean military drills have also triggered an outcry in China, despite assurances that they are aimed at North Korea, not China. The exercises are a response to the sinking of a South Korean warship and are meant to serve as a deterrent.

The U.S. military has repeatedly expressed concern about its lack of understanding about what is driving China's rapid military buildup. In a report last month, the Pentagon said Beijing was expanding its military edge over Taiwan, increasing the lethality of its short-range ballistic missiles.

The report also said China, a growing world economic and military power, was unlikely to be able to deploy large-scale military forces in high-intensity combat operations far from China until well into the next decade.

Morrell stressed that Gates did not want "engagement for the sake of engagement."

"What we are looking for is a resumption of productive, transparent, military-to-military engagement so that we can both gain a better understanding of what our ambitions are, what our intentions are when it comes to our military budgets, how we operate, where we operate and so forth," he said.

China has considered Taiwan -- the self-ruled island across the Taiwan Strait -- as a renegade province since the end of the Chinese civil war in 1949 and insists on unification, by force if necessary.

Since the opening of diplomatic relations with Beijing in 1979, the United States has been obliged by law to provide Taiwan with arms for its self-defense.

(Editing by Todd Eastham)