The 21-year-old central defender has emerged as one of the top young prospects in the Bundesliga this season.
He has not been included in Germany's World Cup squad, but has been called up for their upcoming friendly with Poland which will feature a clutch of the country's most talented youngsters.
Rudiger is contracted to Stuttgart until 2017, but Newcastle are continuing to hunt around Europe for top young talent and he has emerged on their radar.
With Hertha Berlin striker Pierre-Michel Lasogga and Tenerife front-man Ayoze Perez also on their wanted list, it is clear Newcastle's fondness for the continent remains - but Sky Sports understands their summer wish list also has a strong British flavour.
The likes of Fabian Delph, Jack Rodwell and Wilfried Zaha are all believed to feature highly on Newcastle's list of targets as they hope to make up to half-a-dozen acquisitions before August.