New York Gov. Andrew Cuomo's administration and legislative leaders are in talks about returning to Albany early this year for a special legislative session to approve an economic package that may include new taxes on the wealthy, said people familiar with the discussions.

Mr. Cuomo, the Democrat-controlled Assembly and the Republican Senate remain split about the scope of a tax plan. But the talks signal that anti-tax Senate Republicans may be willing to at least consider raising more revenue from the rich.

Lawmakers...