The Daily Star says the Hammers have been linked with a move for the 25-year-old, who has hit 63 goals in 90 starts.
Celtic are desperate to keep their £10m-rated star forward, but know that a chance for him to move to the Premier League could be too tempting.
Hoops boss Neil Lennon said: "He is a brilliant young English player. We would love to hold on to him, it is a priority for me, but if we get a bid in that is good business for the club we may have to think again.
"You don't want to see your best players go, but everyone has a selling point and we're no different to anyone else."