Sept 12 (Reuters) - UK Prime Minister Boris Johnson will attempt to patch up Britain’s frayed relationship with U.S. President Joe Biden"s administration at a White House meeting between the two leaders this month, The Times newspaper reported on Monday, citing sources on both sides. Johnson is expected to hold talks with Biden during a four-day trip to the U.S. for the UN general assembly, which starts in New York on Sept. 21, the report said.