The striker is widely expected to leave the Hawthorns this summer when he will have just one year left on his current deal.
He has been the subject of intense speculation in the last two transfer windows as Tottenham Hotspur were keen on a deal last summer, while the likes of Newcastle United and Stoke were in January.
And now it transpires that the Hammers are also keen on a deal should he be available and have asked to be kept informed of his situation.
They are determined to add a striker to their squad this summer and it seems the Baggies striker is among a number of targets they are looking at.
They would face stern competition for his services though, with the Potters in particular keen on a deal.
According to the same Mirror report, they will once again offer £20million for the 22-year-old in the summer transfer window.
Tottenham Hotspur could also return for him, having settled their difference with the Baggies after the bitter transfer tussle last season.