The incident involved a 24-year-old woman who went into a basement area in Brunswick Street, Glasgow.
It is alleged the man raped her after walking with her in nearby Ingram Street at around 1.25am.
Police scanned CCTV images and carried out door-to-door inquiries following the attack.
Meanwhile, women have been urged not to live in fear following a series of sex attacks in Glasgow.
Police stepped up their hunt for the suspects behind city attacks.
Detective Inspector Craig Willison urged women to continue to go out and enjoy themselves.
He said: "People mustn't feel that they have to avoid going out or enjoying themselves, but be aware that there are predators who will seek out people who appear vulnerable.
"We have additional patrols in the area to provide reassurance to local people and anyone with concerns can raise them with these officers."