The Scotland international was told in January that he could look for a new club, but the 26-year-old remained at the Hawthorns and completed the season with the Baggies.
He played over 20 games for West Brom, but it is still understood that boss Steve Clarke will not stand in his way should an offer come in.
Sky Sports understands that a number of Premier League clubs are ready to make offers.
Amongst them are West Ham, who have previously had bids rejected, and they remain abreast of the situation along with newly-promoted Cardiff City.
Dorrans currently has two years left on his deal with the Baggies.