The 20-year old was recently on a four-day trial with the Baggies and from all reports, manager Roberto Di Matteo was impressed by him.
Haber currently has a year left to run on his Whitecaps contract but the club has said they will let him go if he wishes to pursue his career in Europe.
The former Canada U23 international has already had a stint abroad, spending two seasons with the U19 team at Dutch club FC Groningen before having trials with Leeds United but decided to return to Vancouver earlier this year.
Haber said he was happy with how his trial went but did not elaborate on his chances of making the move to England.
"The trial went well, and I've got only good things to say about the experience at West Brom," is all Haber would say.