It was reported by Netherlands media that the 33-year-old was in advanced negotiations with West Ham, having played under Slaven Bilic with the Turkish giants.
His agent, Niclas Jensen, confirmed the talks via Soccer News Netherlands, and Tulun now claims that he has been informed by a "very reliable source" that the Canada international's prospective switch to East London may already be 'one hundred percent' finished.
''I heard bits about a transfer to West Ham United," he said via Fotomac.
"According to information I received from a very reliable source, [the] Atiba transfer is close, if not a hundred percent finished."
Given the names West Ham have been linked to this summer - the likes of Alexandre Lacazette, Michy Batshuayi and Samuel Umtiti - the arrival of Hutchinson is unlikely to send supporters wild.
But it's another body through the door this summer, with Bilic already tying up a deal for ex-Arsenal midfielder Havard Nordtveit.
Hutchinson, who has 75 Canada caps under his belt, joined Besiktas from PSV Eindhoven in 2013 and his contract expires next summer, meaning that a transfer is unlikely to break the bank.
Bilic has built up a lot of trust with the West Ham fans and, given that Hutchinson is a player he knows well, supporters should expect a useful player, if the move materialises.