The 40-year-old had recently taken Brand house-hunting and while they haven't ruled out a reconciliation, they have agreed to a "cooling down period", Daily Mirror reported.
"Geri was smitten but things have petered out a tad. He isn't ready to settle down so soon after coming out of marriage, whereas Geri is probably more ready to have a relationship.
"She wants a pad and spent Saturday dragging Russell around properties near Devon. It probably seemed a little much. Russell is a huge flirt and Geri won't stand for any nonsense - her friends are telling her not to get serious about him," a source said.
Brand was previously married to pop star Katy Perry.