(Adds byline) TAIPEI, Jan 13 (Reuters) - Taiwan’s central bank has asked custodian banks involved in foreign exchange transactions to exercise restraint in trades as it seeks to rein in the soaring local currency through “moral persuasion”, four sources with direct knowledge told Reuters. The Taiwan dollar’s 5.6% gain against the greenback last year was among the strongest in Asia and its rise extended it to a fresh 23-1/2-year high of 27.944 per dollar last week. It is up nearly 2% this year. Even though exports in 2020 hit a record high by value, the currency’s strength has vexed the government as it risks making shipments from its manufacturing economy less competitive. At the same time, authorities are wary of intervening too heavily in the foreign exchange market and being labelled a currency manipulator by the United States, the most important backer of the Chinese-claimed island. Last month, the U.S. Treasury added Taiwan to a “monitoring list” of countries whose currency practices had caused concern, the first time the island has appeared on the list since 2017. The sources, who spoke on condition of anonymity as they were not authorised to speak to the media, told Reuters that the central bank has met the banks to express their “hope” that their customers spread out their foreign exchange sales. “They must be spread out,” one of the sources said. The central bank did not respond to a request for comment. Another source said the central bank hopes that this will help alleviate the pressure on sales of U.S. dollars. “The big boss has begun their moral persuasion,” the source said, referring to the central bank. The central bank has also sent inspectors to domestic banks to investigate whether exporters are speculating in foreign currency, sources previously told Reuters. Taiwan’s trade-dependent economy has rebounded strongly from the impact of the COVID-19 pandemic, benefiting from global demand for its tech goods as the outbreak forces millions to work and study from home around the world. Exports last year rose 4.9% compared with 2019, to $345.28 billion. (Reporting by Liang-sa Loh; Writing by Ben Blanchard; Editing by Sam Holmes and Kim Coghill)