The Liverpool striker is a target for Rafa Benitez, and the club had been hopeful of securing him on loan.
However, West Brom have emerged as rivals for the 28-year-old, who is looking to play regular football away from Anfield between now and the summer's World Cup finals.
Newcastle's move for Sturridge is in its early stages.
United are understood to be prepared to pay a loan fee of around Â£1.5million and also cover his Â£120,000-a-week wages.
Manager Rafa Benitez is desperate to sign a striker before Wednesday night's transfer deadline.
The club last week had a Â£15million bid for Feyenoord's Nicolai Jurgensen turned down.
West Brom manager Alan Pardew is also looking for a striker, and Sturridge could be left with a choice to make between the two clubs.