A whole host of clubs are chasing the 26-year-old who has netted 14 goals in League One so far this campaign, including Huddersfield, Bradford, Plymouth and Bristol City.
But should either of the two big Scottish clubs make a bid it is likely the player would choose to move there, but Cherries chairman Peter Phillips was quick to play down the speculation.
"We have not been contacted by Celtic or Rangers but they both had scouts at the game on Saturday, which is very unusual," he told the Daily Record.
"Our preference is for James to remain here and he knows there is a contract on the table for him should he stay.
"At the moment, though, he is quite entitled to see what is out there."