The parents of missing Toronto woman Laura Babcock remain hopeful their daughter is still safe, clinging to the belief she simply isn't ready to return home amid new reports about her connection with a man now charged with murder.

Phone records reportedly show that some of Laura Babcock's last phone calls before she disappeared in June 2012 were to Dellen Millard.

Millard, 27, was charged last week with first-degree murder in the death of Timothy Bosma, an Ancaster man who himself went missing earlier this month after going for a test drive with two strangers who expressed interest online in buying his truck. Bosma's charred remains have since been found.

But Babcock's mother said she hopes the disturbing details of that crime and her daughter's link with Millard could just be a grim coincidence.

Linda Babcock remembered Millard as a "polite and handsome" man who, to her knowledge, was never romantically involved with her daughter, although she said the two were friends.

Babcock knew Millard 'for several years,' ex-boyfriend says

She said she only met Millard twice and that he had been to the family's home before to pick up Babcock.

The Babcocks said they are being careful not to let their minds wander to dark places, and still believe that Laura is alive and just doesn't want to come home yet.

If there is any note of optimism to be had, Babcock's family said they are happy that the recent media attention has reawakened interest in the circumstances around their daughter's disappearance.

Babcock's ex-boyfriend, Shawn Lerner, said they had broken up but remained friends right up until she went missing. She had moved out of her parents' house just weeks before vanishing, Lerner said.

"She had been staying with various different friends while she was trying to find more permanent living arrangements," he said.

Police ramping up Babcock investigation

Lerner said Babcock and Millard had known each other "for several years" and that her phone records seemed to indicate she was calling friends for a place to stay temporarily until she found a permanent home.

Lerner said he contacted Millard recently to discuss the phone calls, and that Millard told him Babcock had been calling for drugs and a place to stay — two requests that Millard said he turned down.

Millard's recent arrest has reinvigorated the efforts to find Babcock, Lerner said.

"Once [Millard's] name got out there in connection with this Bosma case, they assigned a couple of new detectives to it," he said. "They basically started the case from scratch."

Police have also questioned Lerner. Eleven months after Babcock's disappearance, he said he's just happy the investigation seems to be back on.

"She's my friend, and we miss her," he said. "We just want her to come back home safe."

Deepak Paradkar, Millard's lawyer, told CBC News that questioning by police has so far focused on the Bosma case.

According to the missing woman's family, Babcock recently started going by the name "Elle Ryan" because she didn't like the name Babcock.

They have no interest in speaking with Millard while police conduct their investigation. 

With files from the CBC's Charlsie Agro