The two celebrities "have been dating for about a month. Having favorable feelings, they are getting to know each other," Kim's agency said in a statement.
Earlier in the day, local online media outlet Dispatch said Rain and Kim began dating in September and that they met every time Rain who serves his mandatory military service was on leave.
Rain's agent Rainy Entertainment said they are not aware of the K-pop star's love life, adding they have never heard of his romance with Kim before the news report.
The 30-year-old Rain, whose real name is Jung Ji-hoon, is one of the most popular male celebrities in South Korea and a well-known star in other Asian nations. He will be discharged from the Army in July.
The 32-year-old Kim, often referred to as the country's most beautiful face, is to star in the upcoming soap opera to be aired by broadcaster SBS.