By Karen Brettell

NEW YORK (Reuters) -The dollar hit a three-and-a-half-year low against the euro and sterling on Thursday in a broad selloff as traders priced in the likelihood that the Federal Reserve will cut rates more than previously expected.

“This week it's definitely been about the Fed, the prospect of easing sooner and potentially more rate cuts,” said Eric Theoret, FX strategist at Scotiabank in Toronto.

Fed Chair Jerome Powell was interpreted as being more dovish this week in testimony to U.S. Congress. He repeated expectations that inflation should rise this summer, but said that if price pressure remains contained "we will get to a place where we cut rates sooner than later."

"Powell kind of opened the door to potentially a July cut," said Noel Dixon, global macro strategist at State Street Global Markets. If the next consumer price inflation release is below market expectations, "I think markets will start to price in the probability of a cut to July."

Fed funds futures traders are pricing in 23% odds of a July cut, up from 13% a week ago, while a cut by September has a 93% probability, according to the CME Group's FedWatch Tool. In total, traders see 66 basis points of cuts by year-end, indicating a potential third 25-basis point reduction, up from 46 basis points on Friday.

U.S. President Donald Trump will nominate a new Fed Chair next year who is expected to be more dovish than Powell, whose term will end in May.

Trump on Wednesday called Powell "terrible" and said he has three or four people in mind as contenders for the top Fed job. The Wall Street Journal reported on Wednesday that Trump has toyed with the idea of selecting and announcing Powell's replacement by September or October.

Analysts say that person could operate as a shadow Fed chair, undermining Powell’s influence.

Dixon said that a shadow Fed Chair could be a problem if inflation reaccelerates and seems to be persistent "because the message there would be that they would discount the inflation."

Chicago Fed President Austan Goolsbee said on Thursday that any move to name a replacement for Powell would have no influence on monetary policy while the nominee awaited confirmation.

The euro was last up 0.51% at $1.1719 and reached $1.1744, the highest since September 2021. Sterling rose 0.62% to $1.3748 and got as high as $1.3770, its highest since October 2021.

The Swiss franc hit a 10-1/2-year high at 0.799 per dollar.

The dollar fell 0.72% to 144.2 Japanese yen.

Investors are also focused on the Trump administration's self-imposed July 9 deadline to negotiate deals that avoid reciprocal tariffs with trading partners.