The Republic of Ireland international will enter the final year of his contract with the Premier League club at the end of the current season, which has tempted the European duo to pursue a summer move.
The Baggies do have the option to extend this by another 12 months, but it is unclear as to whether he is keen to stay at the Hawthorns.
If he actively seeks a move, they may grant his request, but would, likely, rather he moved abroad than to a domestic rivals.
Regardless of this, Liverpool, Tottenham and Newcastle are all interested, and could rival the La Liga and Serie A clubs.
Since arriving in the Midlands from Reading, Long has hit an impressive 16 goals in 58 appearances, but has struggled for first-team opportunities due to a succession of niggling injuries this term.
He is believed to be enjoying lift under manager Steve Clarke, but contract talks are yet to open, leaving his future up in the air.
Lazio considered a January move for the 26-year-old, but failed to make an official approach before the deadline.
They instead swooped for Louis Saha, who was allowed to leave Sunderland by mutual consent.