Postecoglou has confirmed that talks are under way over a possible £6 million deal for the on-loan Spurs central defender.
Carter-Vickers, who will be 24 at the end of this month, is under contract at the English Premier League club until the summer of 2023.
But Postecoglou is hopeful Celtic can meet Spurs’ asking price and agree personal terms with a player who has established himself as a key figure in his side.
“Those are all things we are discussing,” said Postecoglou. “The intimate details of people’s contracts or clauses, all those things need agreement from two or three parties and that’s why we take our time.
“January gives us an opportunity to look at our squad again. We can have a think about what we want to do in this window and the windows beyond.
“Part of that discussion will be around players we have on loan and seeing what decisions we want to make on them.
“A lot of that will depend on the players themselves, if they are happy and want to stay here. We will get round to those discussions.
“Absolutely, I want to keep him. I wouldn’t have brought him in if I thought it was just a short-term thing.
“All the players we have brought in have done so with some thought around building a team. Building a team means more than just 12 months.But as I said a lot of that depends on the player himself.
“Those discussions will happen over the next couple of months. I don’t speak to players about that. People will be well aware that our game schedule has meant that the focus has been on performances, playing well and getting the job done. There is a time and a place for that stuff.”
Celtic are Cameron-Vickers’ seventh loan club, the USA international having spent most of the previous four seasons in the English Championship with spells at Sheffield United, Ipswich, Swansea, Stoke, Luton and Bournemouth.
“He has become an important part of our team and that’s why I was so keen to bring him in,” added Postecoglou.
“Even though he is a young guy, you just have to look at his playing experience. He has had three solid years playing in the Championship playing at good, strong clubs. The Championship in England is a really tough competition, you don’t get through that without having some real quality in you.
“I looked at his track record and I knew we would be getting somebody with more experience than his age would suggest.
“That’s what’s proven to be. The beauty of that is he is only going to get better. And he wants that. He works hard every day, looks after himself and wants to be the best footballer he can be. I knew what I was getting but it has turned out to be a really good move.
“It was a bit of a leap of faith for him because he didn’t have a lot of time to think about it. But I’m sure he would say now that it has been a great move for him. And it’s been a great move for the club.”