The Times report that the "final details on a temporary switch are in the process of being thrashed out" ahead of Wednesday night's transfer deadline.
Sturridge wants to leave Anfield to reignite his stalled career.
Newcastle would have to pay a loan fee of around £1.5million and also cover the striker's £120,000-a-week wages.
United had failed with an improved £15million bid for Feyenoord's Nicolai Jorgensen last week.