Spurs have knocked back an approach from the Swans for Davies, who has emerged as the frontrunner to succeed the sacked Michael Duff as manager of the struggling Championship club.
Duff was a contender for the Swans jobs in the summer before Duff's appointment and the former Wales Under-19 international went on to join Postecoglou's new-look coaching team at Spurs.
Postecoglou says Swansea's continued interest in Davies, who spent most of his career assisting Brendan Rodgers at the Liberty Stadium, Liverpool, Celtic and Leicester, is positive and suggested there could be developments after Sunday's visit of Newcastle in the Premier League.
"I've had a brief discussion with Chris and he knows we've got a busy week so we'll focus on that," the Spurs head coach said on Friday. "He's an outstanding individual, he's done some great work with us and great work in the past. It's not surprising to me that Swansea or other clubs would look at him.
"It's what you want to be honest. You want good people and when you've got good people they're going to attract attention. From my perspective, whatever that transpires to, it's very much in Chris's hands. It's his decision in terms of what he wants to do moving forward and obviously the club will deal with it from there."
Postecoglou added that he is "relaxed" about the prospect of losing the highly-rated Davies and insists stuttering Spurs must not use the uncertainty as an excuse for patchy form.
"I've always been relaxed," he added. "I have said in the past it is part of my role to develop staff and I am really proud of the fact a lot of the guys I've worked with, the reason they are not with me as assistants is because they are senior managers in their own right.
"If you are looking for things that will be disruptive, you can use that as a clutch or an excuse for anything. We lost Harry Kane the day before the season started so there is a disruption, we lost half the squad after one game so there is a disruption. There will always be this.
"You can't work in a vacuum where everything is perfect and for me I have been relaxed in these kind of situations because I have always believed the environment will cover whatever challenges we have if we get it right."
Postecoglou's opposite number this weekend, Newcastle boss Eddie Howe, was on the verge of joining Celtic in summer 2021, only for the deal to fall through due to a conflict over backroom staff.
The Bhoys instead turned to Postecoglou, then an unknown quantity in British football, and the Australian admitted he should probably thank Howe on Sunday.
"Oh absolutely, a sliding doors moment," he said. "There's probably been no bigger decision in me being here [at Spurs] today than Eddie knocking back the Celtic job. I haven't thanked him, I probably should."
Postecoglou revealed captain Heung-min Son could be doubt for the Newcastle game after taking a kick in Thursday's 2-1 defeat to West Ham.
"The last update I got was late last night and he was a bit a sore after the game obviously but the extent of it well need to see how he recovers today," Postecoglou said.
"There were a couple of others with knocks but I don't think anything else insignificant.
"Obviously we got Pape [Sarr] a few minutes last night and I understand him and Richy [Richarlison] came through OK but there won't be anyone else coming back between now and the New Year."