The 23-year-old has impressed this season with 24 goals already to his name and he has stolen the spotlight from team-mate Dean Ashton.
England youth international Ashton was heralded as Crewe's latest superstar in the waiting, but now Hulse is emerging as Dario Gradi's real star this season.
The Baggies had a bid rejected by Alexandra in the summer and it is rumoured they failed again in January before the transfer deadline closed.
West Brom's chief scout Bobby Hope watched Hulse score in Crewe recent 2-2 draw at Notts County.
However, one worrying point for The Hawthorns outfit could be the interest being shown by their local rivals Wolves.
Woves assistant manager John Ward and chief scout George Foster were present at the same game as Hope, to watch Hulse.
The First Division outfit also have the benefit of that they can still buy players as they are not bound by the transfer window like the Premiership clubs.
Whether Wolves would be tempted to make a bid before the end of the season remains to be seen, but even if they do Crewe are unlikely to listen to any offers as they are embroiled in the Division Two promotion race.
