The Bournemouth winger is hot property after assisting 14 goals in the Premier League last term – a total only Eden Hazard could beat.
He has failed to put pen to paper on a contract extension with his current deal expiring at the end of next season.
Bournemouth are looking for around £30m for Fraser’s signature but they could be tempted to cash in to avoid losing him on a free.
Arsenal, who are working with a limited transfer budget this summer, are likely to bid nearer £20m.
But Gunners bosses will be boosted by Fraser’s desire to move to the Emirates Stadium.
The 25-year-old admitted in April it was “very nice” to be linked with Arsenal.
And, according to Football Insider, he has now told friends that he wants to join the north London giants.
Fraser was quizzed about his future after helping Scotland to a Euro 2020 qualification victory against Cyprus on Saturday.
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“The lads have been asking,” he told BBC Sport.
“I don’t know myself so there’s no point thinking about it, wherever I’ll be, I’ll be.
“I don’t know what is happening. I’m not just saying that.”
Fraser added: “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.
“If you think about anything else, I’ll probably have a bad game.”
Meanwhile, Arsenal have reportedly reached an “agreement” to sign Dalian Yifang ace Yannick Carrasco.
Club bosses are now attempting to strike a transfer agreement with Carrasco’s club to bring him back to Europe, according to Italian journalist Nicolo Schira.
“Arsenal is defining for Carrasco from Dalian Yifang,” Schira wrote on Twitter.
“Contacts ongoing with Chinese club to finalise the last details of the deal.
“The Belgian player has already an agreement with Gunners.”