Fresh from watching his side beat Arsenal 3-1 on Saturday, Albion boss Tony Pulis jetted to Italy to watch Skriniar in action against Juventus as he ponders a summer swoop.
Skriniar has made 27 appearances for Samp this season and has caught the eye of clubs throughout the rest of Europe, including the Baggies.
The defender is under contract until 2020 so Sampdoria are under no pressure to sell, but they could still struggle to keep hold if they receive an offer they cannot refuse.
Skriniar's versatility is also a big attraction as he can play as a defensive midfielder as well as a left-sided central defender, something which Pulis is in need of.
Gareth McAuley is expected to sign a new 12 month contract in the summer but at 37 years of age Pulis is keen to bring in a younger defender to step into his boots.