RadarOnline.com reported Thursday that Roberts, 55, would be resigning for personal reasons.
But the source said the report is "completely untrue." There is "no medical issue, no issue at all," the source said, adding that there is not even a 1 percent chance that Roberts is considering resignation.
RadarOnline.com later published an update saying that Roberts will be staying on the bench.
Fox News' Shannon Bream contributed to this report.