The Cherries winger is hot property after assisting 14 goals in the Premier League last term – a total only bettered by Eden Hazard.
He is about to enter the final year of his contract and has failed to agree an extension.
Bournemouth are ready to cash in if they receive an offer worth £30m.
Arsenal, however, are reluctant to meet their asking price due to their limited transfer budget.
Despite the fevered transfer talk, Fraser insists he has not held talks over any potential move.
“The likelihood is I will be at Bournemouth for another year,” he said.
“And what will happen, will happen.
In other Arsenal news:
“That is all I can really say about it. No one has really spoken to me about it.”
Fraser admitted in April it was “very nice” to be linked with Arsenal.
He has reportedly told friends that he wants to join the north London giants.
The Scotland international has admitted, however, that he is not spending too much time pondering his future.
“Wherever I’ll be, if it’s Bournemouth or if it’s at somebody else, then all you can do is try your best and enjoy football,” he said after helping Scotland to a Euro 2020 qualification win against Cyprus.
“If you think about anything else, I’ll probably have a bad game.”