The 53-year-old star, who filed for divorce from second wife Michelle Rounds in February following their split last November, is said to have quietly started romancing the Oscar-winning actress two months ago.
A source close to Tatum, split from ex-husband John McEnroe in 1994 after eight years of marriage, told the Daily Mail Online: ''Tatum has spent some time at Rosie's compound over the past month. She went back to LA but will fly east again in the next few days.''
The pair went to see the Broadway musical 'Hamilton' together early last month and were later seen enjoying dinner at Da Silvano in New York City.
Another insider told Star magazine: ''They aren't quite ready to go public with their romance. They've known each other for a while, but the secrecy of their dating has made it more exciting.''
But a spokesperson for the former 'The View' co-host told E! News: ''They're [just] friends and [have] been for a number of years.''
Tatum, who has three children, Kevin, 29, Emily, 24, and Sean, 27, with retired tennis player John, opened up about her sexuality in the September issue of Harper's Bazaar, writing: ''In a the physical sense, I'm not attracted to men right now at all.
''Dating women is exciting to me, and this is turning me on.''
''I dated in the heterosexual world up until about four years ago, when I started thinking about dating women - just thinking about it.''
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