President Donald Trump is leaning toward naming Jerome "Jay" Powell as Fed chair but remains undecided, a source told CNBC.

For weeks, Powell has been considered the front-runner for the job as the president considers who will steward the central bank when Janet Yellen's term expires in February. However, the competition has turned into a derby in which various candidates have moved to the front only to get pushed back in the wake of news developments.

On Saturday, a source also told The Wall street Journal that Powell was Trump's likely pick for the Fed chairmanship.

Powell, a current Fed governor, has the advantage of presenting Trump with a chance to break from the Yellen Fed yet maintain many of the same policies that have kept the stock market rally intact and interest rates low.

"If Trump believes Yellen's approach is best for keeping market levels growing, he is going to seek a Fed chair who can carry on her mantle but under the Trump brand. The best non-Yellen Yellen is Powell," Beacon Policy Advisors said in a report Friday morning.

Powell was appointed to the Fed in 2012 to fill an unexpired term that won't end until 2028. He has emerged as a compromise candidate as Trump considers reappointing Yellen or moving to a starker alternative like Stanford economist John Taylor, who would be expected to push for higher rates and a faster reduction in the Fed's $4.5 trillion balance sheet.

The president has praised Yellen in recent days, but the chance to make a break from the past could prove too enticing.

"Given the president's propensity for comparing himself against President Obama and seeking to continually undercut his legacy, choosing the Obama-appointed Yellen for another term would not give Trump the satisfaction of leaving his own mark on the Federal Reserve," the Beacon noted added.

"Some Senate Republicans are making grumblings about Powell and his allegiance with Yellen's decision making while at the Fed, however, Senate Republicans will not obstruct a Trump nomination of Powell."

Trump previously has indicated he will make a choice before he leaves on his next foreign trip next Friday.