The 26 year-old stopper is rated in the €13 million class and has attracted an approach from Zenit St Petersburg in recent days.
German media sources say Höwedes is weighing up his future in Germany and is pondering moving abroad in the summer.
Along with Zenit, Höwedes is also being watched by United, with manager David Moyes having had his scouts active in the Bundesliga this season.
Höwedes has spent his entire career with Schalke and penned a deal to 2017 twelve months ago.
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