Ms Davis told CNN that the department had reviewed all available video footage and found there was no probable cause to warrant Nichols’ arrest.
Police have previously said that a “confrontation” occurred as they approached Nichols’ vehicle, and he fled on foot. He was taken into custody after a second “confrontation”, during which he received critical injuries.
Nichols, 29, died in hospital three days later.
The officers have been charged with second-degree murder. Their bodycam footage is due to be released at 6pm (7pm ET) on Friday.
In an interview with CNN, Ms Davis told Don Lemon that the department had conducted a thorough review of bodycam footage, and CCTV from the route that Nichols had been driving.
“We’ve taken a pretty extensive look to determine, you know, what that probable cause was, and we have not been able to substantiate that,” she said.
“It doesn’t mean that something didn’t happen, but there’s no proof.”
Ms Davis said the bodycam footage was “about the same, if not worse” as the Rodney King’s beating by LAPD officers in 1991.
In a separate interview, Shelby County District Attorney Steve Mulroy said there were discrepancies between the police report and bodycam footage.
“That’s the kind of thing that I think the ongoing federal investigation might be particularly interested in,” Mr Mulroy said.
Speaking at a press conference at the Justice Department on Friday, Attorney General Merrick Garland described the assault on Nichols as “deeply disturbing”.
FBI director Christopher Wray said he had personally viewed the tape and said he was “appalled”.
Mr Wray said his “heart goes out” to Nichols’ family.
He added that law enforcement was prepared for any civil unrest following the release of the footage.
The Tennessee Bureau of Investigation has opened an investigation into Nichols’ death, while and the US Department of Justice and FBI are also pursuing separate civil rights probes.