A stranger who sexually assaulted a 16-year-old girl in her own home in Melbourne's south-east offered her money to compensate her for the attack, police say.

It comes as the father of the teenager broke down as he made a public appeal for the attacker to come forward and described his daughter's strength.

Police have released this image of a man wanted over the Cheltenham sex attack.

The girl was sleeping in a bungalow attached to the family's home in Devon Street, Cheltenham when she woke to find a man sitting at the end of her bed at 2.30am on Thursday.

What followed was a "bizarre and disturbing" conversation where the attacker, who claimed he had a knife - which was never revealed - offered money to compensate for the assault and told the girl his parents would be disappointed in him, sex crimes squad Detective Senior Sergeant Jason Walsh said.