Treasury yields rose suddenly on reports that Kevin Warsh, a former Fed governor, met with President Donald Trump on Thursday to discuss his potential nomination as Fed chair.

to succeed Fed Chair Janet Yellen and bond traders view him as a hawkish choice. The PredictIt probability market Friday gave him odds of more than 45 percent, well ahead of Yellen.

The temporarily edged up to a high of 1.4787 percent after the report from The Wall Street Journal. CNBC later confirmed the meeting took place. The rose to 2.318 percent. Yields, which move opposite price, reversed some of their immediate gains after further reports that other candidates remain under consideration for the job.

"The key factor that the market is focusing on is he would be less accommodative than Yellen has been as a baseline in terms of QE [quantitative easing], the path of tapering and the potential path of rate hikes. All of that should be reconsidered if Warsh is a serious candidate and it sounds like he is," said Aaron Kohli, director fixed income strategy at BMO.

Administration officials have said that for the chairmanship. Yellen's term ends in February, and Trump has made favorable comments about her.

However, analysts note that Yellen is very vocal about the Fed's regulation of the financial industry and Trump would like to see some regulation loosened. Warsh, who has a Wall Street and government background, would be seen as someone who would be more interested in deregulation. His father-in-law, Ronald Lauer, is also a close associate of Trump.

Also reported to have been considered are Stanford University economist John Taylor and former BB&T CEO John Allison. Analysts say also believed to be in the running are Fed Governor Jerome Powell and Randal Quarles, nominated by Trump as the first-ever Fed vice chair for supervision.

Politico's Ben White, a CNBC contributor, reported Friday that and that Powell is being seriously considered.

"[Warsh] seems very pro-tax reduction and in favor of streamlining regulation. I think that President Trump wants two things out of the Fed chair," said Mark Cabana, head of U.S. short rate strategy at Bank of America Merrill Lynch. "One, he wants a dove on policy and two, he wants a deregulator. Yellen is a dove, but she's not going to be a deregulator. She told us that at her Jackson Hole speech."

But the dilemma for Trump, who has said he likes low interest rates, is that the candidates who are more likely to push more lax regulation are those who might move faster to normalize rates.

"It becomes muddier because most people that sit in that seat have to moderate their views based on reality, and the reality is that inflation isn't moving," said Kohli. "As much as we believe he would taper aggressively, and raise rates aggressively, it might not come to that."

Kohli said the long end of the curve may not see rates rise that much if Warsh is a serious contender because he might move quicker to reduce the Fed's balance sheet or raise interest rates faster. Either of those would be considered policy moves that could slow economic growth.

Warsh helped engineer the Fed's response to the financial crisis but he was outspoken about his concerns over quantitative easing, or the Fed's purchases of bonds, after the crisis. He resigned from the central bank in 2011.