The police, however, said the evidence do not point to the opening batsman's personal involvement in the case in which one of his friends, Sandeep Jude Selliah, 26, was arrested.
Gunathilaka, 27, was not aware of what took place between the Norwegian woman who had complained of rape on Saturday night and his friend after which his friend was arrested, they said.
However, Gunathilaka had booked two rooms at the hotel on the night of the incident and had violated Sri Lanka Cricket's code of conduct of players by staying out longer hours, the police said.
Gunathilaka was later suspended by Sri Lanka Cricket for breach of discipline and therefore will not figure in the 5-match ODI series against South Africa starting Saturday.
His friend has been remanded in custody and was to make a magisterial court appearance today, the police said.
"Gunathilaka has said he was asleep and was not aware of what had taken place between his friend and the Norwegian woman," said the policeman on condition of anonymity.
Notably, Selliah is a British passport-holder of Sri Lankan origin.
"The police are not pressing charges against Gunathilaka at the moment, but the case record will be presented to a magistrate on Thursday," the officer told AFP.
The police said the Norwegian woman had left Sri Lanka after making the rape complaint. The incident took place at the hotel where both the Sri Lankan and the visiting South African teams are staying.
The cricket board will conduct a disciplinary hearing after police investigations are over.