The 28-year-old joined Schalke from Bochum in 2011 and has since gone on to make 74 appearances for the German side.
Renowned for his crossing and set-piece ability, Fuchs is also a veteran of the Austrian national team and has represented his country on 57 occasions, scoring once.
Interest from Sunderland could indicate that Gus Poyet has given up on his chances of signing Marcos Alonso from Fiorentina.
Alonso enjoyed a successful loan spell at the Stadium of Light last season and was thought to be at the top of the Uruguayan manager's transfer targets this summer. But with alleged interest from West Ham United, and Fiorentina seemingly undecided on the Spaniard's future, Sunderland may now be looking at other targets.
Fuchs was reported to have attracted attention from Fulham during last season's January transfer window.
According to the Mirror the defender was available for around £2million, although the West London side eventually failed in their attempts to lure the Austrian international to Craven Cottage.
A fee as low as £2million is likely to interest Sunderland, but any potential deal for the defender could still carry some substantial risk.
Fuchs underwent surgery on his right knee in late March and although he is expected to be fit in time for the new season, he may not prove to be the smartest acquisition should any complications regarding his injury arise.