SEOUL, June 19 (Reuters) - South Korea's foreign exchange authorities view the 1,385 level as a line in the sand for the won versus the dollar, two sources involved in the policy discussions told Reuters on Tuesday, citing recent measures to arrest the currency's weakness.

The Bank of Korea and the finance ministry were preparing measures to intervene in the USD/KRW spot market had it breached the 1,385 level in late-May, the sources said, requesting anonymity due to the sensitivity of the matter.

"The authorities were waiting to see if the won weakens beyond the 1,385 level to decide the timing of measures to support the won," one of the sources said, referring to his conversations with FX authorities.

A fast weakening of the won has been causing headaches for policymakers in Asia's fourth-largest economy as the currency lost 6.5% against the dollar so far this year.

The won hovered around 1,381.6 per dollar on Wednesday.

On May 31, the finance ministry said the Bank of Korea and the National Pension Fund are in talks to expand their FX swap line of $35 billion, a program that allows the fund to borrow the central bank's forex reserves instead of buying dollars in the onshore currency market.

(Reporting by Cynthia Kim; Editing by Sherry Jacob-Phillips)