Batts, former chief in Long Beach, has two years left on his contract in Oakland. Neither candidate would confirm the report for the Bay Area News Group.
The differences are stark, with Batts an African-American from SoCal and Moore a white, Northern Californian.
Rick Callender, former head of the city's NAACP, told the Mercury News: "Obviously the city manager deserves a feather in her cap for a choice which can begin to restore the faith of the entire community and the police officers in the leadership of the department."
The choice is a tough one, given the recent - and pending -- cuts to the polie budget, as well as the battering the force has taken over its perceived slights to the minority community.
A decision is expected early next month.