* Dollar weakens further after weaker jobs data * Euro undeterred by Jan flash PMI numbers * Sterling sets its eyes on $1.40, near 3-yr high * Graphic: World FX rates tmsnrt.rs/2RBWI5E LONDON, Feb 19 (Reuters) - The U.S. dollar slipped further on Friday and the euro rebounded after disappointing U.S. data dented optimism for a speedy recovery from the COVID-19 pandemic, while sterling edged towards the $1.40 mark. The U.S. currency had been rising as a jump in Treasury yields on the back of the so-called reflation trade encouraged investors back into the greenback. But an unexpected increase in U.S. weekly jobless claims soured the economic outlook and sent the dollar lower overnight. On Friday it traded down 0.1% against a basket of currencies, the dollar index now at 90.474. The string of soft labour data is weighing on the dollar even as other indicators have shown resilience, and as President Joe Biden’s pandemic relief efforts take shape, including a proposed $1.9 trillion spending package. The euro rose 0.2% to $1.2113. The single currency showed little reaction to German and French flash purchasing manager index data, which unsurprisingly showed a slowdown in activity in January. Despite the recent rise in U.S. yields, many analysts think they won’t climb too much higher, limiting the benefit for the dollar. ING analysts said that “the rise in rates will be self-regulating, meaning the dollar need not correct too much higher.” They see the greenback index trading down to the 90.10 to 91.05 range Sterling has been the standout performer in 2021 and on Friday rose to $1.3987, an almost three-year high amid Britain’s aggressive vaccination programme. Given the size of Britain’s vital services sector, analysts say the faster it can reopen the economy the better for the currency. The dollar bought 105.46 yen, down 0.2% and a continued retreat from the five-month high of 106.225 reached Wednesday. Many analysts expect the dollar to weaken over the course of the year as it has traditionally done during times of global economic recovery, though it might take some time to develop. “It looks to me like there’s some exhaustion in that just-straight global reflation theme,” leading the dollar to trend largely sideways for now, said Daniel Been, head of FX at ANZ in Sydney.