Fanatik's Orhan Yildirim (h/t Calciomercato, via Metro's Will Giles) said the former, who once played for Chelsea, is valued at around £14.5 million, and the same source (h/t talkSPORT) believes the latter would cost slightly more, around £15 million.
Fans of the Gunners may have heard of Ozyakup before―he used to play for Arsenal but moved to Besiktas in 2012.
The duo has been pivotal in Besiktas' fast start to the 2015-16 campaign, with the team currently leading the Turkish Super Lig, having won all but two of their first seven matches. Tore in particular has looked mighty impressive, handing out five assists and adding one goal in those matches, per WhoScored.com.
As shared by OptaCan, the strong production isn't a fluke:
Ozyakup has been almost as good, with four assists and one goal, incredible numbers from a central midfielder, per WhoScored. The two have thoroughly enjoyed playing with summer arrival Mario Gomez, who has set the Turkish league alight in his first couple of matches:
The Super Lig has gained a reputation for favouring older foreign stars over developing young talent of its own in previous names, with the likes of Gomez, Robin van Persie and Nani all moving to Turkey, but the nation produces plenty of impressive talent, regardless.
As shared by football writer Karadeniz Firtinasi, the young nucleus of the national team looks promising, and he ranked both Besiktas stars among some of the best footballers Turkey have produced in years:
A January move seems unlikely, but both are ready to make the step up to one of Europe's elite leagues, and next summer could provide the perfect opportunity.
The question is where they'd fit in at Arsenal. Ozyakup spent time with the Gunners both as a member of the academy and as part of the senior squad, and manager Arsene Wenger didn't see enough at the time to keep the 23-year-old around.
He has since developed into a fine midfielder, but the Gunners have plenty of those. Ozyakup almost looks like a copy of Santi Cazorla, who has become one of Arsenal's most important players and won't be dropped from the starting XI anytime soon.
Meanwhile, Tore is more of an advanced option, playing most of his minutes as a right-winger. The Gunners could use some more pace and creativity out wide, but Alex Oxlade-Chamberlain is already struggling to find regular minutes―Tore's situation wouldn't be any different.
The jump straight to Arsenal would perhaps be too great for the duo, who would be better off moving to a mid-table side. Milliyet (h/t Calciomercato, via Metro's Will Giles) said Aston Villa watched Tore during Besiktas' 3-2 derby win over Fenerbahce, and a move like that could be perfect for the winger.
Meanwhile, Slaven Bilic was the man to originally sign Ozyakup from Arsenal in 2012. He's now in charge of West Ham United, a club that could always use another creative midfielder. TalkSPORT's report may talk about Ozyakup and the Gunners' need for a defensive midfielder, but the Turkey international is far more attack-minded; not someone Arsenal desperately need.
That said, both are promising young players worthy of an investment for any club. If Arsenal were to sign one or both, it would be smart signings with an eye on the future. It's just far more likely that one of the smaller Premier League clubs swoops in with the promise of regular playing time, allowing the two to continue their development.