The actor told People that he remembers being a 12-year-old like his son, and quipped that he's concerned for that reason.
"I'm trying to digest it all, and I'm just trying to remember what it's like to be in a teenage romance," he said. "And what I remember scares me as a father!"
However, Douglas added that he is not an "over-protective" dad, saying: "Dylan is a great kid and I trust him. He's having fun and conducting himself very well."
Douglas, who revealed that he has liked Dylan's girlfriends so far, continued: "I want him to know to always be polite and respectful and just don't try too hard. If he asks me for specific advice, I'll have a long talk with him."
Douglas also revealed that his marriage to Catherine Zeta-Jones is still "doing well", saying: "She is more beautiful than ever inside and out. I support her with everything and she is simply the best."
Douglas will star as the legendary pianist Liberace in new HBO film Behind The Candelabra opposite Matt Damon, who reportedly told Zeta-Jones that he pictured her when he was kissing her husband for the movie.
Steven Soderbergh, who directed the project, has suggested that it was "too gay" for Hollywood.
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