TOKYO (Reuters) - Sterling extended gains on Thursday amid expectations a long-elusive Brexit deal was imminent, raising hopes the UK can avoid a turbulent economic rupture on New Year’s Day. The dollar was on the back foot in holiday-thinned trading as hopes for an agreement that would protect some $1 trillion in annual cross-channel trade from tariffs and quotas sapped demand for the safest assets. The British pound strengthened 0.2% to $1.3525 early in the Asian day after surging 0.9% in the previous session to snap a three-day losing streak. The dollar index was at 90.255 following Wednesday’s 0.3% slide. The euro strengthened 0.1% to $1.22025, adding to a 0.2% gain overnight. The riskier Aussie dollar traded at 75.802 U.S. cents following the previous session’s 0.8% jump. While there has been no official confirmation from either side that the months of negotiations had reached a conclusion, a senior British government source said Prime Minister Boris Johnson was poised to do a trade deal with the EU, after media reports said the agreement had already been done. A source at the EU’s executive Commission said talks were still under way, and another British government source was also cautious, saying negotiations were ongoing. “This time it really does appear that a deal will be struck just in time for Christmas,” Westpac macro strategist Tim Riddell wrote in a client note dated Dec. 24. “If a deal does transpire on 24th December, GBP is likely to make further gains” toward $1.40, “but potential for a more substantial move towards 1.4500 now seems unlikely given how positions exhaustion is so prevalent.” The Brexit headlines overshadowed U.S. President Donald Trump’s demand for changes to a coronavirus aid bill, effectively threatening a government shutdown next week. The dollar index has lost more than 6% this year as investors bet the U.S. Federal Reserve will keep its monetary policy ultra-accommodative and fiscal stimulus will speed an economic recovery in 2021. Expectations for further declines by the dollar are helping buoy stock markets and emerging-market currencies. “The fact that equity indices traded mostly in the green this morning reflects a consensus expectation that Trump will sign the budget into law – though he could wait until the eleventh hour,” Jane Foley, senior FX strategist at Rabobank in London, wrote Wednesday in a research note. “If this doesn’t happen the USD could benefit from safe haven buying,” but longer term the U.S. currency will weaken to $1.23 per euro over the course of next year, she said.