During a lunch meeting Tuesday with the Republican Senate leadership, the president asked for a show of hands vote on who they would like to see him nominate to lead the central bank when current Chair Janet Yellen's term expires in February.
One report indicated that Stanford economist John Taylor was the victor.
Trump didn't say who came out on top specifically, "but I think Taylor won," Sen. Tim Scott, R-S.C., told reporters, according to Bloomberg.
Trump has indicated he will release the name of his nominee before his next foreign trip Nov. 3. According to remarks he made over the weekend, the president is most seriously considering Fed Governor Jerome Powell and Taylor, though he acknowledged that giving Yellen a second term is not out of the question.
Those two, Powell and Taylor, were the choices for Trump's informal Fed poll, CNBC confirmed.
Sen. John Cornyn, a Texas Republican, informed media outlets of the initial Trump request, according to multiple tweets from news outlets.
As the news circulated through Twitter, Fed watchers buzzed about Trump seeking GOP input on the Fed pick.
OMG. Next there will be 800 numbers for each candidate, as we vote for AMERICA'S TOP CENTRAL BANKER.
Prediction markets believe Powell is likely to be the nominee. A recent CNBC poll confirmed that, though respondents said they'd generally prefer Yellen to get the nod. Taylor's stock shot up on PredictIt after the news about the straw poll, though Powell remained in the lead.
Some leading Republicans have favored Taylor, believing he would be more likely to depart from the course Yellen has set out. Taylor believes in a rules-based approach to monetary policy, which would dictate specific conditions under which the central bank would raise or lower rates.
Under Yellen, the Fed has followed a data-driven approach that has drawn criticism for being more arbitrary and subject to nonspecific standards.
Taylor is most well known for developing a rule that specifically lays out where the Fed's benchmark rate should be. The fed funds rate is used to determine interest rates for most consumer debt.
According to the Taylor Rule, the funds rate should be closer to 3 percent than the current level of 1.15 percent.
--With reporting by Ylan Mui