Police investigating the mysterious off-campus murder of an Auburn University freshman say they have witnesses to the crime and have set up a state and federal task force to hunt down the killer, and sources tell FOX News that the detective work is paying off.

Local reporters told FOX News' Greta Van Susteren Thursday evening that authorities are said to be close to an arrest in the shooting death Tuesday of Lauren A. Burk, 18, though no suspects have been named.

Burk died Tuesday night at a local hospital of a single gunshot wound to the head. About a half hour after she was found, her car burst into flames.

WBRC's Dave Bondy told Van Susteren that Lee County Sheriff Jay Jones had said investigators are investigating the possibility Burk knew her attacker, but the sheriff wouldn't say whether police had confirmed that detail.

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In a separate case, another Georgia college student — this one from the University of North Carolina at Chapel Hill — was also shot in the head and killed this week.

Student body president Eve Marie Carson, 22, was found dead on Wednesday. Authorities and school officials identified her as the shooting victim on Thursday.

Marietta, where Burk was from, and Carson's hometown of Athens are about 67 miles apart.

"I don't have anything at this point to indicate that this is related," said Auburn Assistant Chief of Police Tom Dawson at a news conference Thursday. "I've had my investigators contact authorities there, but there's nothing to connect the two cases."

Auburn police said they had solid leads and were aggressively hunting down Burk's killer, but they declined to disclose what they've discovered so far.

"We do have several leads we are investigating — strong leads," Dawson told reporters. "I'm not trying to keep you from getting information, but we are in the middle of an extensive investigation of somebody's daughter who has been murdered."

He said he'd "dramatically" beefed up patrols on and around Auburn University's campus. The task force was established because police want the murder mystery solved.

"It has increased our manpower," Dawson said. "I wanted the brightest minds on this case."

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A $10,000 reward was offered in the Burk case by Alabama Gov. Bob Riley's office.

"Everything that can be done must be done to bring this killer to justice," Riley said in a statement Thursday.

Riley said he hopes the $10,000 reward will "encourage someone who can help police solve this crime to come forward. Our prayers go out to Lauren's family and friends during this difficult time."

His second-in-command said the governor's office wanted answers as soon as possible.

"We hope we can resolve this as quickly as we can," Lt. Gov. Jim Folsom told FOX News on Thursday. "This is a real shock to the state of Alabama and the Auburn community."

Folsom said he couldn't offer much in the way of specifics about the crime.

"Details are sketchy," he said.

Police on Thursday were reportedly questioning several witnesses and "persons of interest" who might know something about what happened to Burk.

The teen's sorority sisters from Delta Gamma and other friends mourned her Thursday, describing the Marietta, Ga., native as sweet, friendly and well-liked and saying they have no idea who would have wanted her harmed.

"I can't imagine someone she knew doing this to her," Burk's close friend Jay Seyfried, a classmate from Walton High School, told MyFOXAtlanta.

Auburn Campus reacts to killing of Lauren Burk

Auburn Police Capt. Tom Stofer said the death was being investigated as a homicide. There were no immediate arrests.

"We have not named a suspect and are still investigating leads," Stofer said, adding that officials are remaining tightlipped because of the circumstances of Burk's death.

School officials said there was no indication that others were in danger.

Burk was found wounded on Alabama Highway 147 around 9 p.m. Tuesday, about three miles off campus, and Auburn police said her Honda Civic was discovered engulfed in flames at the campus about 20 minutes later. She was taken to East Alabama Medical Center, where she died Tuesday night.

University officials advised students in an e-mail around noon Wednesday that there was "no indication of additional danger to campus or student safety." But the school said the police presence on campus had been increased.

"As soon as we know more we might release it, but what information we have now we're holding it close to our chest," he said.

Burk's death has stunned the Auburn campus in Lee County, Ala., where the mood was subdued and students walked around mostly in pairs, according to MyFOXAtlanta.

"It's just really scary knowing I came here, feeling safe here on this campus," Auburn student Katrina Kreimer told the news station.

Auburn President Jay Gogue, who was out of town Wednesday, released a statement: "We are so saddened by this situation, words simply aren't adequate. This is a close-knit community that rarely experiences such a tragedy."

An on-campus prayer vigil for Burk was being organized by her friends and a memorial was being planned by her Delta Gamma sorority.

"Considering the unexpected and disturbing nature of the situation, the women of Delta Gamma have reacted with immense concern," the sorority's national office said in a statement. "Delta Gammas across the country offer hope and friendship to Lauren's family and all who have been affected by this tragedy."

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FOX News' Catherine Donaldson-Evans and The Associated Press contributed to this report.