By Benjamin Kang Lim and J.R. Wu

BEIJING/TAIPEI (Reuters) - Taiwan President-elect Tsai Ing-wen's diplomatic honeymoon with China could be shortlived if she allows the Dalai Lama to visit the self-ruled democratic island that Beijing claims as its own, two senior political sources said.

China regards Tibet's exiled spiritual leader as a separatist, and Ma Ying-jeou, the outgoing president who favors closer economic ties with the mainland, refused the Dalai Lama entry several times since his last visit to Taiwan in 2009.

On that occasion Ma did allow him in, although he did not meet the 80-year-old.

With invitations pending from Buddhist groups that are likely to be renewed after Tsai and her pro-independence Democratic Progressive Party easily won January elections, the incoming leader faces a dilemma, said a Taiwanese source close to the DPP and another with direct knowledge of the matter.

"The Dalai Lama could visit as early as around national day," said the source close to the DPP, requesting anonymity because of the sensitivity of the matter.

The Republic of China, Taiwan's official name, marks its national day on Oct. 10.

Since sweeping to victory at the polls, Tsai has vowed to seek to maintain the "status quo of peace and stability" with China, Taiwan's biggest trading partner, and Chinese state-run media have noted her pledges.

Since the election, Beijing has also warned against any moves towards formal independence and said it would defend its sovereignty.

Tsai, who takes office on May 20, must decide whether to let the Dalai Lama in and risk riling China at a time when tensions in the region have already been raised over rival claims to the vital waterways of the South China Sea.

The Dalai Lama, who won the Nobel Peace Prize in 1989, fled into exile in India in 1959 after an abortive uprising against Communist rule.

China has accused him of being a separatist, but the monk says he only wants genuine autonomy for his Himalayan homeland.

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Tsai could try and seek a compromise, the sources said, by convincing Beijing to keep dialogue open, rather than stonewalling her, in exchange for allowing the Dalai Lama into Taiwan but not meeting him one-on-one.

The DPP said in a statement it was not aware of an invitation for the Dalai Lama to visit Taiwan.

The Dalai Lama's office in India, where he lives in exile, said: "His Holiness the Dalai Lama has no plans to visit Taiwan at the present time".

China's Taiwan Affairs Office did not respond to a request for comment.

The Dalai Lama congratulated Tsai on her "remarkable" victory, according to www.dalailama.com.

"It is indeed encouraging to see how firmly rooted democracy has become in Taiwan," the Dalai Lama wrote. "It is a model and source of inspiration to those who aspire (to) freedom and accountable leadership."

Beijing and Taipei have been diplomatic and military rivals since their split in 1949 after the Nationalists lost the Chinese civil war and fled to Taiwan. But trade, investment and tourism have blossomed during outgoing Ma's eight-year rule.

(Additional reporting by J.R. Wu in TAIPEI, Ben Blanchard in BEIJING and Abhishek Madhukar in DHARAMSALA, India; Editing by Mike Collett-White)