The Manchester United youngster may be heading out on loan next season, with Tony Pulis reportedly interested in bringing him to the Hawthorns.
Wilson exploded onto the scene at United last season with a brace on his debut in a win over Hull City.
He has made his fair share of appearances this season under Louis van Gaal, featuring 16 times despite the arrival of Colombian star Radamel Falcao.
And the 19-year-old has two goals to his name, having netted away to QPR in the league and against Cambridge United in the FA Cup replay at Old Trafford.
The Mirror is reporting that West Brom boss has good contacts with Wilson's agent and that he has been watched by the club's chief scout for the Under-21 side recently. If that was the game against Manchester City on May 12, the scout would have been suitably impressed as the youngster scored one and made another in an impressive 4-0 victory.
The Baggies may have rivals for Wilson's youngster though. They aren't the only Midlands club who are chasing the young striker, with the Mirror also reporting that Aston Villa are interested in helping Wilson get some more Premier League football under his belt.