NT Police said Jefferson Lewis, 47, was recently released from prison and was staying at the Alice Springs home at the time of Sharon's disappearance on Saturday night.
"We do believe Sharon has been abducted," Acting Commander Mark Grieve said in Darwin on Monday.
Sharon was reported missing from her Old Timers Aboriginal town camp residence about 1.30am on Sunday after being put to bed.
A search will resume after about 50 police officers, emergency services and a helicopter were unable to locate her on Sunday.
Police say Mr Lewis had been staying at the home where Sharon lived and went missing at the same time.
"He is believed to have been in the area around that time and staying at the residence," Mr Grieve said.
"He currently remains one of the few people who were in Old Timers camp at the time and who has not made themselves known to police, nor have police been able to locate him."
The man was not in prison for child-related offending before being released, police said.
"Considering himself and Sharon went missing at around about the same time, it certainly brings about those suspicious circumstances and we'd like to speak to him about that," Mr Grieve said.
"If he is involved, we certainly hope that no harm has come to Sharon."
Sharon's mother has been provided with support, he said.
He called for any information from the public that may help locate Sharon.
"Obviously it's a terrible situation to have such a young child go missing," Mr Grieve said.
"We're over 24 hours now so it'd certainly be my worst nightmare as a parent."
The Northern Territory Police Tactical Response Group was expected to travel to Alice Springs on Monday morning to assist.
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