Mitu was murdered seven months ago.
On Thursday, Mitu's parents met investigating officer and Chittagong Detective Branch Assistant Commissioner Md Kamaruzzaman.
After the meeting, her mother Shahida Mosharraf Neela told journalists, "I have talked to the one who has the mobile phone.
"He said 'I am a CNG driver'," she said.
When she asked where he had found it, she said he replied 'at Motijheel'.
He would often send 'missed calls' from the number, the mother said.
Asked if Babul was cooperating in the case, his father-in-law Mosharraf Hossain evaded a direct response.
"That is for the IO to say. We will say this, today we have come, I think Babul should have accompanied us," he observed.
Investigating Officer Kamaruzzaman later said an 'expert team' was probing the mobile phone issue.