Mohamed Elyounoussi is set to leave Southampton this month.
The Norway attacker has been made available by Saints with the European transfer deadline to fall on September 2.
VG says Besiktas, along with LaLiga duo Seville and Celta Vigo, are all in contact.
And Saints boss Ralph Hasenhuttl confirmed to TV2: "We want to give everyone the chance to play. If he does not feel comfortable sitting on the bench, or maybe in the stands sometimes, he has goals other than us."
Elyounoussi still has four years to run on his contract.