The Premier League side have already made a move for the Portuguese's teammate.
Sporting Lisbon's Adrien Silva
The Express and Star reports that the Baggies have already made a move for Sporting striker Islam Slimani this summer, and while it remains to be seen whether they follow up the £14.6m bid that was rejected earlier this month, it appears that they have added his teammate to their list of targets.
Sporting's Islam Slimani has already been the subject of a West Brom bid this summer
The interest in the pair is arguably a sign of Tony Pulis' desire to get on with things after a fairly quiet summer at the Hawthorns.
The Baggies have so far made just one signing, and are running out of time if they hope to add to that number before the window shuts.
However, they appear to be facing competition from their Premier League rivals for Adrien's signature. The Sun claimed earlier in the month that Everton and Tottenham were amongst the sides keeping an eye on the player, so they may perhaps be alerted if West Brom decide to make a move.
The 27-year-old has been a key man for Sporting over the last four seasons, and despite playing in midfield, he is more than capable of contributing goals, scoring at least seven times in the league in each of the last three campaigns.
And with West Brom perhaps lacking depth going forward, he would surely be an excellent addition if they could get a deal done.
West Brom manager Tony Pulis