After signing from Hull for £10.2m just seven months ago, Robert Snodgrass has been told he is free to leave West Ham.
Sunderland boss Grayson has already expressed an interest in the 29-year-old with whom he worked during his spell at former club Leeds.
Grayson revealed last week that his side had missed out on the signing of Bournemouth's Max Gradel despite reaching an agreement with the Cherries.
When asked if he was interested in signing Snodgrass, the Black Cats' boss said: "When people like him become available you would be foolish not to consider it.
"Again, that would be a deal dictated by finances. Can we do it? Who knows, but we might ask the question."