It's largely come down to a two-horse race between Summers, a former Treasury secretary, and Fed Vice Chairman Janet Yellen for the next Fed chief.
It is widely expected that the current Fed Chairman Ben Bernanke will resign by the end of the year as his term ends in January. President Obama has already said that Bernanke has "already stayed a lot longer" in the role than he expected. Those remarks came in an interview with Charlie Rose on PBS in June.
Who might take the reins from Bernanke has been an undertone in the market and at the Fed's recent meeting in Jackson Hole, Wyoming.
Summers didn't attend the Jackson Hole meeting but his name was tossed around the sidelines.
Several Fed officials, who spoke on condition of anonymity, told Reuters that they did think Summers was Obama's clear favorite, though they had a few doubts.
"Has he devised a strategy to be effective within the institution?" one asked.
Some insiders also expressed concern about Summers' close ties to Wall Street.
The race for the next Fed chief comes amid another big point of discussion for policy makers - when to begin tapering the Fed's $85 billion per month bond-buying program. There has been much speculation that it will begin in September.
- Reporting from CNBC's John Harwood, with contributions from Reuters