Stubblefield, whose body has never been found, was studying criminal justice, and had law enforcement aspirations.
The Chicago Tribune reports investigators believe Stubblefield was strangled to death and stabbed in the head.
In 2015, police spoke to Fuller about his missing girlfriend, and he denied the couple were together or that the unborn child was his.
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Police searching for Stubblefield found her car abandoned in Gary.
They also found Stubblefield's broken eyeglasses and her red and black shoes in the area.
According to the reports, a woman Fuller who had been involved with in late 2015 was interviewed by detectives last summer.
She allegedly told authorities Fuller had admitted to killing Stubblefield.
Police have yet to discuss a possible motive.
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