Richarlison has scored seven goals in as many Premier League games ahead of his first return to former club Everton on Saturday.
The Brazilian struggled after joining Spurs in a £60million deal from the Toffees in summer 2022, scoring just once in the League last season, but he has appeared sharper and more confident since having surgery on a pelvis problem in November.
Postecoglou says Richarlison still has room for improvement but played down the suggestion that the 26-year-old was making a case to be Spurs' first-choice centre-forward long-term.
"I’ve never thought in those terms because if you do, you box yourself in," Postecoglou said.
“What I want is for Richy to keep improving, and keep developing his football and becoming a real force for us and we’ll see where that takes us.
“Because as this year alone has shown us, whatever plans or designs I had about which kind of formation I was going to play and which players were going to play a part in that, that pretty much went out the window after the first 15 minutes at Brentford when [Cristian] Romero gets concussion and I’ve got to make a change.
“I’ve never thought in those terms. For me, it’s about trying to get players to fulfil their potential and with Richy I still think there is growth there.
“If it keeps growing, well we the football club will be the beneficiaries of it.”
Postecoglou's squad options are finally returning to a position of strength after months of disruption caused by injuries, and James Maddison's return to fitness is a particular boost.
The England playmaker is pushing to start for the second time this week at Goodison Park and Postecoglou says his "upbeat" character and leading-man energy are important in the dressing room.
"He is exciting to watch, he’s a creative player and invariably supporters love those kind of players who can do something a little bit different," Postecoglou said.
"Part of it is the way he carries himself. Madders likes to be, for want of a better term, in the spotlight. In the right way.
"He doesn’t shy away from the responsibility. He’s in the team to create and be a force and he embraces that, and I think our supporters enjoy to see one of their own stand up in that kind of environment.
"It’s a combination of things. And he’s just a loveable little rogue mate. Apparently.
"He doesn’t mind a moan. When he was injured he wasn’t great. He’s a very upbeat guy and not short of a word which is not a bad thing.
"Characters and personalities like that are very important in a dressing room, provided they back it up on the field.
"For me that’s always the ultimate measure, and he’s more than backed it up on the field."
But Postecoglou added that different types are also important to a harmonious and successful squad, and picked out defenders Emerson Royal and Ben Davies, and back-up goalkeeper Fraser Forster, as examples to the rest of the players.
"As much as there might be a universe where that exists, you can’t have 11 James Maddisons in your team," Postecoglou said.
"You need other kinds, different types of players, that’s the chemistry we’re all after where you’ve got a bit of everything in your team.
"That’s the challenge for every manager, how do you fit all these pieces into a beautiful puzzle? Sometimes we try and jam them into spaces where they don’t fit.
"If you watch Emerson Royal train every day, you’d think he plays every game. He’s just outstanding with his attitude and demeanour around the place.
"There’s no time for anyone to feel down. When you see a guy like Emerson, and we’ve got a few in that boat this year like Fraser or Ben, they train so hard every day, always have the greatest disposition in terms of their demeanour, it doesn’t give anyone else an excuse to not feel up for it.
"Those are the kind of things that make a difference to your dressing room, as well as your leaders.
"If you’re going through a tough time or maybe you’re battling with a few things, you see these kind of people, your leaders and others who just lift you up."