Willock, 27, had been expected to leave St James' Park after limited opportunities last season and entering the final year of his contract.
Besiktas made an approach, but Newcastle rejected the offer after new head coach Matthias Jaissle decided the midfielder remained part of his plans.
Jaissle's faith has been rewarded, with Willock scoring three goals this season and taking on a more prominent role in the Newcastle side.
Adali, however, has not abandoned the pursuit and revealed just how far Besiktas went in their attempts to complete the transfer.
“There were players we couldn't sign in the summer. Our manager wanted Joe Willock from day one, it was Willock, Willock, Willock,” Adali said.
“Nobody knows this, but I brought Willock's whole family to Istanbul.”
The Besiktas president said Willock's family even selected a house in Istanbul, while the player held multiple video calls with manager Vincenzo Italiano and football director Onder Ozen.
“They even picked out a house, and they had video calls with [manager] Vincenzo Italiano and Onder Ozen, [football director] at least ten times. Furthermore, we went to see the player in person twice.”
Adali believes Besiktas can still complete the move during the January transfer window.
“He could sign in the mid-season. They asked for £20m. We can sign in January, and I will. Joe Willock was the player the coach wanted but was missing. We really need him there.”
Willock's contract situation makes the January window particularly significant, as he will be able to sign a pre-contract agreement with overseas clubs from January if he has not extended his Newcastle deal.
The midfielder has previously spoken about the change in his fortunes since Jaissle's arrival.
“I feel valued. It is like my fifth year at the club, and I am really maturing in the way I think towards the team and getting older,” Willock said.
“There are a lot of young players coming in. It is a different role for me this season. I want to help others and push on in my career as well.”
His Newcastle United revival has not ended Besiktas' interest. Adali's comments make clear that the Turkish club intend to try again when the transfer window reopens.