The Baggies have confirmed the wantaway hit-man has been interesting them for some time, but their proposal for him has been refused.
With Albion set to lose unsettled striker Jason Roberts, manager Gary Megson clearly wants to strengthen his attacking options.
"We've had Rob Hulse watched many times," said Albion chairman Jeremy Peace.
"He's a very promising talent and we've registered our interest with Crewe."
Meanwhile, Canaries chief execute Neil Doncaster has revealed the Carrow Road side have made a move for the in-demand ace.
"We have submitted a written offer to Crewe for Rob Hulse and we are waiting to hear back from them," said Doncaster to First News.
