CLEVELAND, Ohio -- The investigation into the shooting death of 12-year-old Tamir Rice by a Cleveland police officer could soon be handed over to an outside agency.

The Cleveland Division of Police's use of deadly force investigation team has been collecting evidence and conducting interviews since Cleveland police officer Timothy Loehmann shot Tamir outside Cudell Recreation Center Nov. 22.

But Cleveland Safety Director and former police Chief Michael McGrath has been in talks with Cuyahoga County officials to hand the investigation over to the sheriff's office, city spokesman Dan Ball said.

"Not only this investigation, but we would like a different, outside agency to handle all deadly use of force cases," Ball said. "But nothing's set in stone."

Cuyahoga County Sheriff's spokesman John O'Brien could not be reached for comment Wednesday.

Loehmann shot Tamir after a 911 caller alerted police that someone was in the park playing with an airsoft-type gun, waving it around and pointing it. Cleveland police officer Frank Garmback -- with Loehmann in tow -- drove a cruiser onto the grass less than 10 feet away from Tamir, who began walking toward the car.

As Loehmann jumped from the still-moving car, Tamir lifted his shirt, revealing the handle of what police said they thought was a handgun. Loehmann opened fire within two seconds, hitting Tamir once in the stomach. The boy died early Nov. 23.

Many aspects of the shooting have come under scrutiny and activists, as well as attorneys representing Tamir's family, have called for an outside agency to investigate the incident.

The calls became even louder after a report from the U.S. Department of Justice lambasted the city for the way the department for how it trains officers in using deadly force, investigates uses of deadly force and disciplines officers for using force.

If the city and county reach an accord, it will be the second high-profile Cleveland police killing to be scrutinized by an outside agency in two years.

The investigation of the Nov. 29, 2012, chase and shooting of Timothy Russell and Malissa Williams was conducted by the state's Bureau of Criminal Identification office under Ohio Attorney General Mike DeWine.

East Cleveland had jurisdiction over the shooting because it happened in their city, and officials there asked for BCI's help.

But Cleveland leaders bristled with DeWine's assertion that the chase - which involved more than 90 cars, 60 officers and ended in 137 shots fired by police officers into Williams' car - resulted from a "systemic failure" in the police department.

At a Dec. 11 conversation with reporters, Cleveland Mayor Frank Jackson said he "lost confidence" in the state's Bureau of Criminal Investigation to investigate shootings after that and said the FBI doesn't have jurisdiction to conduct investigations.

"The best way to do it is to have external eyes look at anything regarding use of force cases," Jackson said.

The administration has approached the sheriff's office to conduct those investigations, Ball said.

"We want this just as much as anybody," Ball said.

Dennis Willard, spokesman for incoming Cuyahoga County Executive Armond Budish's transitional team, said Budish has participated in multiple meetings between Cleveland and sheriff's office officials since the shooting, but could not specify the content of the meetings.

The agency ultimately tapped to lead the investigation will give its evidence to Cuyahoga County Prosecutor Timothy J. McGinty's office. Prosecutors will present the case to a grand jury, which will decide whether to indict Loehmann and Garmback on criminal charges.

McGinty successfully convinced a grand jury to indict officer Michael Brelo on involuntary manslaughter charges earlier in 2014 for his role in the deaths of Russell and Williams, but grand jury decisions not to indict officers in New York and Ferguson have led to nationwide protests and calls for reform to police-involved shooting investigations.