(Adds comment from White House, background on Yellen and Cohn)
WASHINGTON, July 11 (Reuters) - President Donald Trump is increasingly unlikely to nominate Federal Reserve Chair Janet Yellen next year for a second term, and National Economic Council Director Gary Cohn is the leading candidate to succeed her, Politico reported on Tuesday, citing four people close to the process.
Politico said sources in the White House, the Treasury Department and on Capitol Hill said that if Cohn decides he wants the job, he is likely to get it.
"It's Gary's if he wants it, and I think he wants it," Politico quoted one Republican whom it said was close to the selection process as saying.
A few Senate Republicans may express reservations about Cohn but he would probably receive widespread support, a senior congressional Republican aide said, according to Politico.
In response to a query from Reuters, White House spokeswoman Natalie Strom said: Gary is focused on his responsibilities at the NEC.
Cohn, a Democrat and former Goldman Sachs president, did not work on Trump's campaign and only got to know him after the November election.
Yellen took over from Ben Bernanke as Fed chair in February 2014 with the U.S. economic recovery from the 2008 financial crisis still on shaky ground. She has made no secret she puts a priority on growth in jobs and wages and a broad recovery in U.S. household wealth.
Yellen begins two days of congressional testimony on Wednesday on the Fed's semi-annual report on the state of the U.S. economy.
During last year's election campaign, Trump accused Yellen of accepting orders from then-President Barack Obama to keep interest rates low for political reasons, and he said he would replace her as Fed chair because she is not a Republican Party member.
But in an interview with The Wall Street Journal in April, Trump said Yellen was "not toast" and that he respected her.
(Reporting by Eric Beech; Editing by David Alexander and Leslie Adler)