Slovakia's Milan Skriniar in action against Germany
Baggies boss Tony Pulis is said to have watched the 22-year-old in La Samp's 1-0 defeat to Juventus on Sunday.
The Daily Mail claims Skriniar is one of Italian football's "brightest prospects", having arrived at Stadio Luigi Ferraris from Zilina last summer.
The Slovakian - who wears the number 37 shirt made famous by compatriot Martin Skrtel at Liverpool - was a target for German trio Bayern Munich, Borussia Dortmund and Schalke 04 ahead of the January transfer window, according to Calciomercato.
The Daily Mail reports West Brom are prioritising the centre of defence for strengthening this summer, and the Baggies have also been linked with Championship pair Marc Roberts (Daily Mail) and John Egan (The Sun).
Barnsley's Marc Roberts in action
The contracts of Hawthorns stoppers Gareth McAuley and Jonas Olsson are due to expire this summer, while Marc Wilson and Brendan Galloway are expected to return to their parent clubs at the end of their current loan deals.
Would Skriniar be a good signing for West Brom?