Delegates at the Skybridge Alternatives(SALT) Conference believed Geithner at the Fed would mean more accommodative and pro-stimulus measures from the central bank.
(Read more: Kudlow: Geithner to the rescue?)
Geithner offered "measured comments" to the audience at theSkybridge Alternatives (SALT) Conference during a closed door discussion onWednesday, steering clear of commenting directly on whether he was keen onbeing the next Fed chairman, according to people who heard his remarks.
Gary Kaminsky, vice chairman, wealth management at Morgan Stanley,moderated the discussion and told CNBC after the event that there was a "big,unanimous decision" amongst the audience of hedge fund managers that "they'dlike to see [Geithner] take that job if offered."
"There was a strong feeling that if [Geithner] decided to take theFed job, everybody here in Singapore believed it would be the most bullish thingfor markets, for continuity of Fed policy," Kaminsky said.
(Read more: Wall Street worries about consumer as Congress squabbles)
The Fed last week maintained its $85-billion-dollar-a-month asset purchase program – a surprise move for markets, which had anticipated a scaling back of the massive monetary stimulus.
The decision on who will replace Bernanke as the head of the Federal Reserve is being watched closely in the context of the tapering debate.
(Read more: Summers withdraws his name for Fed chair)
Earlier this month former U.S. Treasury Secretary Larry Summers withdrew his name for consideration as a candidate to be the next Fed Chairman.
Summers and Fed Vice Chair Janet Yellen were thought to be the top two contenders for the job and it was widely speculated that Summers was Obama's top choice.
Still, some conference attendees put the chances of Geithner as the next Fed chief at zero.
"He has enough baggage in the last five years that he will face opposition, particularly from the Democrats, but probably from the Republicans as well," said John Lilley, executive director at Taurus Wealth Advisors.
But he added, "It would be less damaging to markets than someone like Summers, who is considerably more hawkish."
By CNBC's Sri Jegarajah; Follow him on Twitter