The Scotland international enjoyed a superb season last time out, scoring seven goals and providing 14 assists in the Premier League.
Arsenal have been keeping tabs on the forward in recent months, with Fraser about to enter the final 12 months of his Bournemouth contract.
The Cherries value the former Aberdeen man at £30m, which would represent a large chunk of Arsenal’s overall transfer budget.
And Fraser has now suggested that he will not be moving to the Emirates Stadium this summer.
“The likelihood is I will be at Bournemouth for another year,” he said.
“And what will happen, will happen. That is all I can really say about it. No one has really spoken to me about it.”