There is likely to be no shortage of interest in the Scotland international - who impressed for Hull City during the first half of the last campaign - but Grayson has hinted that he is keen on a reunion with a player who he worked with at Leeds United.
The 47-year-old told reporters: "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."
Snodgrass has made eight starts and seven substitute appearances for West Ham in the Premier League.