Harper, 19, is out of contract this month and has failed to agree an extension at the Hawthorns.
New boss Slaven Bilic is keen to hold talks with the youngster in a bid to persuade him to stay at the Championship club and play a key role in the push for promotion.
But the Baggies are in danger of losing Harper for just a small compensation fee.
Liverpool and Tottenham are also interested in the teenager, who has been with West Brom since the age of 12.
Harper made 16 appearances for West Brom last season as they made the Championship play-offs.