The wing-back spent last season on-loan with Genoa.
Postecoglou said: "I think with Djed, for me, we've restarted pre-season and we're assessing him on his own merits. He's a Tottenham player. To be fair to him, I think he's been very, very good for us in this pre-season , in terms of the way he has trained and his general attitude. But a lot of these things are in the hands of the players themselves, in many respects, and I think Djed is in that boat.
"I think there is an opportunity for him here, for sure. Thinking about building a team, he would definitely be someone who could (contribute) with the characteristics that he has. Last year I thought there was a possibility , but it didn't work. For this type of thing, I think sometimes players are really waiting for direction when they can really take control of their own direction."
He added: "Djed is here. He is a Spurs player. He is a very good player who adapts to our football and therefore the decision concerns both him and me. As you can see, he has been very good in pre-season and on tour. He has impressed all the coaches, not just me. For some of them it's their first time working with him and they're all very impressed with him. Maybe he's learned a couple of things about himself in the last couple of years and hopefully we can reap the benefits of that."