Rose has struggled to make a breakthrough into the first-team as Benoit Assou-Ekotto has become the first choice left back at White Hart Lane.
The England Under-21 player is determined to play regular first-team football and could be tempted by a move to the Hawthorns.
West Brom’s new head coach Steve Clarke is ready to bring in several new faces and is looking for a new left-back after Nicky Shorey was released by the club last season.
Rose has shown he can compete at the highest level and few could forget his memorable strike against Arsenal on his league debut.
Clarke may have to wait until Tottenham confirm their new manager before the two clubs can start negotiations over a possible move for the 21-year-old.