The Gunners are looking to add to their squad in the summer after missing out to Manchester City in the title race this season.
West Ham captain Declan Rice is Arsenal’s No1 target but manager Mikel Arteta is looking at reinforcements elsewhere.
Boey is understood to be of interest to Arsenal and full-back is an area that the club want to strengthen.
As well as Boey, the Gunners hold an interest in Valladolid right-back Ivan Fresneda and explored a deal for the 18-year-old in January.
Boey is four years older than Fresneda and the 22-year-old Frenchman has been a regular for Galatasaray this season as they close in on winning the Turkish top flight.
Galatasaray are thought to want around £20million for Boey, who is understood to be open to the idea of moving to the Premier League.
Arsenal currently have three right-backs on their books, with Ben White the first choice there this season.
Takehiro Tomiyasu has been out injured since March after injuring his knee but he hopes to be back for pre-season.
Cedric Soares spent the second half of this season on loan at Fulham and is due to return to Arsenal this summer.
“We have to nail everything that we do and we have to seek excellence in everything that we touch and participate in, to have a big impact at the club,” said Arteta, when speaking about the summer transfer window.
“I think the competition is going to be even harder than this season. In my opinion, it’s been the hardest of the 22 years that I’ve been in this league.
“In order to do that, we have a really promising plan. We may have to reflect a little bit, take a step back, make sure this is the right one and go again with more determination and hunger in the tummies to do even better.”