According to the National Enquirer, Foster started an affair with screenwriter Cynthia Mort after the pair worked together on Neil Jordan's 2007 drama.
"The affair heated up last year and the pair have been quietly seeing each other since then," a source is quoted as saying.
Foster's 14-year relationship with Bernard had long been an open secret in Hollywood but the actress only revealed publicly that she was a lesbian last December.
The couple have two boys and are still living together in Hollywood. However, Foster is planning to move out.
The source added: "They will continue to raise the boys together."
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