During an appearance on Watch What Happens Live Thursday, Green, 27, confirmed she's no longer in contact with Rose, 42, after the pair split in July. When asked if things are "amicable" between the former couple, Green said she's not so sure about fostering any kind of relationship with Rose moving forward.
"He wants to be, but that's having his cake and eating it too. So, no," Green told host Andy Cohen. "I'm not about that. Not for right now, at least."
In addition, Green said she'd "have to assume" Rose was not entirely faithful to her during their relationship — not counting the infamous "stairwell" incident, in which Rose admitted to kissing another woman.
Green revealed she's not currently dating after her breakup with Rose, but there is one Bravo-sphere single she has her eye on.
Cohen asked if he could help set her up with anyone in the Bravo universe, to which Green named "Blonde Tom" — or Tom Schwartz from Vanderpump Rules. Schwartz, 39, is in the midst of a divorce from wife Katie Maloney — so, he is single.
"I met him at NBC and Friends and he was just a doll," Green said, adding, "He's very lovely." She ended the TV pickup with finger guns to the camera, and Cohen reminded Green they'll likely cross paths at the upcoming Bravocon convention.
PEOPLE first reported Green and Rose's split in July. According to sources, Rose's infidelity was the leading reason for the split.
"Shep has a real issue with monogamy and refused to commit to Taylor, telling her that he doesn't want to be with just one person and change his lifestyle," one source said.
"She's incredibly hurt, but she knows that she deserves a guy who will fight for her, not one who is so selfish," another insider added. "He'll regret this."
Rose has yet to comment on the split.
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Southern Charm airs Thursdays at 9 p.m. ET on Bravo.