The midfielder almost joined Leicester City in the summer but the move fell through at the 11th hour.
The Portugal international had been ready to join the Foxes for £21m, but Sporting then shifted the goalposts and demand the 27-year-old's £38.5m release clause was met.
That forced Leicester to cancel the deal and now, according to A Bola, they could lose out to West Brom.
The Baggies have recently been taken over by Chinese investors and they are reportedly ready to fund any move for Silva.