Two officials spoke on condition of anonymity Monday because they were not authorized to discuss the matter ahead of an official announcement.
Seven million sign-ups was the original target set by the Congressional Budget Office for subsidized private health insurance offered through new online markets.
That was scaled back to 6 million after the disastrous launch of HealthCare.gov last fall.
The 7 million-mark would beat expectations.
It was in sight on a day when the administration saw surging consumer interest in the nation's newest social program, but struggled with repeated website glitches.