The Baggies were represented at the Portuguese league game at the Alvalade stadium and, having been linked to Carrillo in March, it is highly likely that they wanted to watch the 21-year-old forward again.
It is possible that they had eyes for other targets with Norwich City signing Ricky van Wolfswinkel also on show.
But Canaries officials are confident they have a watertight agreement with Sporting for the player in the summer – whichever division they end up in next season.
Carrillo, who cost Sporting £800,000 from Alianza Lima just under two years ago, has scored only one goal in 20 appearances for the Lisbon club this season and his last start came back in February.
QPR and Galatasaray were the only other foreign clubs with scouts at the game, but it is thought that the Baggies would be in the driving seat should they decide to make an offer.
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