Nicole was engaged between Tom and Keith

Nicole Kidman says she was engaged to a mystery man in between breaking up with Tom Cruise and marrying Keith Urban. "I didn't really want a relationship," Kidman says in Vanity Fair. "I just wanted my kids to have me, and I didn't feel comfortable having some person in that small hubbub. And then I got engaged to somebody...but it just wasn't right. I wasn't ready. We weren't ready." When pressed for details, the actress said, "I get engaged and I get married - that's my thing. I'm interested in a very, very deep connection." Sources say the mystery man was Lenny Kravitz: "They were even house-hunting together for a while." A rep for Kravitz said, "I cannot confirm or deny it." The Oscar winner says she has no regrets about her marriage to Tom Cruise. "My agents told me, 'Once you become Mrs. Tom Cruise, you do know your career is going to die,'" says Kidman. "I was appalled. I was like, 'Hello? I'm in love, and I don't care if it's shooting myself in the foot. I'd much rather be married and have a family."