The Baggies face a crucial January as they look to land the players Sam Allardyce believes can keep them in the Premier League.
Strengthening the spin of the team is understood to be the head coach’s priority with a defender, defensive midfielder and striker at the top of his list.
But Allardyce is also determined to bring in quality players who have the experience and character needed for a relegation battle.
Snodgrass certainly fits that bill with the 33-year-old known to be a positive influence both in the dressing room and on the pitch.
It is understood West Ham are willing to listen to offers for the winger this month with manager David Moyes eager to reduce the size of his squad and lower the wage bill.
Snodgrass has made just three brief substitute appearances for the Hammers this season.
He is also out of contract in the summer meaning he is likely to be available for a nominal fee.
That fee will be crucial with Albion likely to want to sign Snodgrass on a permanent basis rather than on loan.
Premier League rules state you can only sign two players on domestic loans.
Albion already have one in Conor Gallagher who has impressed ever since arriving from Chelsea.
And it is highly likely they will want to use their second loan to improve the spin of the team – with Leicester’s defensive midfielder Hamza Choudhury known to be a player under consideration.
Snodgrass has previously enjoyed success in the West Midlands following a loan stint with Villa in 2017.
The set-piece expert also won 28 caps and scored seven goals for Scotland before announcing his retirement from international football in 2019.