The Glee star, who has previously been linked to Cameron Diaz and Kelly Brook, stated that he didn't want to have a lover "in the business".
He told Fabulous magazine: "Having had several girlfriends, I know what I don't want. Don't want someone in the business."
However, the 32-year-old accepted that dating an "ordinary" woman would have its own challenges.
He said: "Bringing someone into this life scares me. For an ordinary person to be thrust into hanging out with me and having their picture taken all the time is a big ask.
"I'm having such an incredible time in my life and I'd really love to share that with someone and have someone to talk about my day with. You never know who's round the corner."
Asked whether he was looking to settle down soon, Morrison added: "I can't see myself without children. Because I'm an only child, the thought of a big family scares me, but I also know what just being one feels like. Two would be good. Maybe three."
Morrison, who in February was reported to be dating actress Olivia Munn, recently claimed that he is too busy to have a relationship.
> Morrison 'uncomfortable being a sex symbol'