(CNN) It has been weeks since little Maleah Davis went missing and the man overseeing the search for the Houston girl has no hope searchers will find her alive.
"We really believe we have a little girl that has been murdered," police Chief Art Acevedo told reporters on Thursday. "We believe she's out there somewhere and we want to bring her home.
"I can sit here and say we're going to find her alive, but I'd be lying to you."
Acevedo said suspect Derion Vence, who was caring for Maleah while her mother was out of town, has not been cooperative with investigators.
In early May, Vence told authorities that a trio of Hispanic men knocked him unconscious and abducted Maleah, who is 4, while they were driving to the airport to pick up Maleah's mother. Within days, authorities say his story began to unravel.
Court documents suggest that blood from the apartment Vence shares with Maleah's mother is "consistent" with DNA taken from Maleah's toothbrush, and surveillance footage shows that Maleah never left the apartment.
Vence was arrested earlier this month and booked into Harris County jail on suspicion of tampering with a human corpse, according to police. Court documents indicate a "substantial likelihood" Vence will be charged with murder.
Acevedo said that the reward in the case has increased to $10,000.
He urged people to be on the lookout for anything that is of the ordinary, especially in areas near bayous, hiking trails, wooded areas and places that may not be heavily traveled.