The 'Fool's Gold' actress - who was previously married to Black Crowes rocker Chris Robinson and has dated cyclist Lance Armstrong and actor Owen Wilson - couldn't be romantically involved with someone who kept secrets.
She said: "Other people can have 'understandings' and not discuss things and turn blind eyes - but I couldn't exist in a relationship that wasn't honest and sacred in that department."
Meanwhile, the 29-year-old star - who has a four-year-old son, Ryder, with Chris - also revealed she will be cutting back on spending this Christmas and is planning to make many of her own gifts.
She said: "I think it's a really weird time and I think that everyone is feeling it."
"We've always been pretty crafty anyway. We all knit. The girls knit. This year I'm doing these great big knit... well, actually I shouldn't even talk about it because I can't say it!"
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