The Liverpool striker is a target for Rafa Benitez, and the Magpies had been hopeful of securing him on loan.
However, West Brom have emerged as favourites for the 28-year-old, who is looking to play regular football away from Anfield between now and the summer's World Cup finals.
Baggies boss Alan Pardew has earmarked Sturridge and Watford hitman Troy Deeney as his main strike targets as he looks to guide the club away from the relegation zone.
It would be a bitter blow for Benitez if he missed out on Sturridge. The striker was understood to be set to travel to Tyneside for talks today, but didn't make the journey amid reports he has decided to have a medical at the Hawthorns instead.
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United were understood to be prepared to pay a loan fee of around £1.5million and also cover his £120,000-a-week wages.
Benitez is desperate to sign a striker before Wednesday night's transfer deadline. Newcastle last week had a £15million bid for Feyenoord's Nicolai Jurgensen turned down.