Dorrans signed a new three-and-a-half year contract with the Baggies in January, with the option of a 12-month extension.
However, his displays have alerted a number of top-flight clubs, including West Ham.
Hammers co-owner David Sullivan said he wants to strengthen the squad after securing their Premier League future following a 3-2 win over Wigan on Saturday.
However, the former Birmingham supremo also conceded the club will listen to offers for any player other than Scott Parker.
"Under no circumstances will Scott Parker be sold and we will be buying more than we are selling," he told the Daily Mirror.
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