The Baggies reportedly sent scouts to watch the winger in action in a recent international against Paraguay and are pondering a summer move.
Montero has a release clause of £3.5million in his contract with his Mexican club and Baggies boss Steve Clarke could make his move in the coming weeks.
Meanwhile, West Brom are involved in the battle to sign Udinese striker Matej Vydra on loan after the forward's impressive loan stay with Watford last year.
Albion are also keen on Arouna Kone and Franco Di Santo, who is now a free agent after deciding to end his stay with relegated Wigan.
Kone is still under contract with the Latics and is believed to favour a move to Everton, but Argentine Di Santo could be convinced to move to the Hawthorns.