By Dhara Ranasinghe and Linda Pasquini

LONDON (Reuters) -A battered dollar is taking another beating as investors, unnerved by fresh signs of an erosion in U.S. central bank independence, waste no time in pushing the greenback back to its lowest levels in over three years.

President Donald Trump on Wednesday called Federal Reserve Chair Jerome Powell "terrible" in his latest attack on the Fed chief and said he has three or four people in mind as contenders for the top Fed job.

The dollar was back at multi-year lows against a basket of other major currencies on Thursday, erasing a brief respite provided by safe-haven flows related to Middle East tensions earlier in the week.

Down 10% so far this year and set for its worst year since 2003, the dollar was expected to weaken further as renewed concern about Fed independence comes amid increased expectations for rate cuts and a looming July 9 deadline for trade agreements.

"We are short the dollar in this environment, where there is an erosion of institutions," said Kaspar Hense, a senior portfolio manager at RBC BlueBay Asset Management. Being 'short' a currency means holding bets it will fall in value.

"This is not currently 100% in the price, and it would still move markets if someone like Hassett or Bessent would get the job in order to cut rates, ignoring fundamental risk," Hense said.

The leading contenders for next Fed chief reportedly include former Fed Governor Kevin Warsh, National Economic Council head Kevin Hassett, current Fed Governor Christopher Waller, and Treasury Secretary Scott Bessent.

"I think the market is pricing in President Trump appointing someone who at least at first sight appears more sympathetic to his cause," said Societe Generale chief FX strategist Kit Juckes.

Comments earlier this week meanwhile by Fed policymaker Michelle Bowman, recently tapped by Trump as the Fed's top bank overseer, that the time to cut rates is getting nearer weakened the dollar as rate-cut expectations rose.

Traders now price in a nearly 25% chance of the Fed cutting rates in July compared to 12.5% last week.

Trump's confrontations with longstanding allies over trade and security, and his attacks on the Fed, have revived questions in Germany around its holdings of central bank gold, some of which is stored at the New York Fed.

And European Central Bank supervisors are asking some of the region's lenders to assess their need for dollars in times of stress, gaming out scenarios in which they cannot rely on tapping the Fed under the Trump administration, Reuters reported last month.