He also likely had scratches or cuts on his face, neck, hands and arms that day, police said.
They added that they believe him to be the same man seen driving a dark coloured SUV in the area around the time that the young jogger was killed.
The public is warned not to confront anyone suspected of being the killer, as he is to be considered dangerous. Instead, they should contact police.
Police have not revealed how they acquired the DNA, saying only that they got it during the course of their investigation.
It is also not clear exactly how the DNA was used to build the profile.
Marcotte vanished on an afternoon run while on a visit to the home her mum Rosanna, lived in off Brooks Station Road. Marcotte lived in New York.
Her naked body was found at around 8.20pm in woodlands near the home. She had been sexually assaulted, and her hands, feet and part of her head were burned.
It's believed she was killed some time between 1pm, when she left her mom's home, and 4pm.