Victory at Manchester United on Sunday would take Tottenham into the top four, possibly as high as third, and only three points behind halfway leaders Liverpool.
With Germany striker Timo Werner joining on loan this week and Romanian defender Radu Dragusin on a six-year deal and the likes of Cristian Romero, James Maddison and Manor Solomon nearing returns from injury, Postecoglou believes Tottenham can enjoy a better second half of the season than the first.
Asked on Friday whether that means they are in the title mix, the former Celtic boss said why not?
"If I say 'no' you'd turn round to me and say 'come on Ange'. By definition, we are aren't we? So, yes we are and I've said all along that until the point where you're not, why discount the possibility?" he told reporters.
"We've gone through a really tough period and we're hanging in there. We had four games when results went against us, but we've clawed our way back. We're still in there.
"Our performances have been pretty consistent. With the conditions we've overcome, with the conditions we've made, we certainly we feel we can finish the season stronger.
"We've got a platform here to kick on."
Whether Tottenham can go to the next level will largely depend on Postecoglou drastically improving results against the so-called big six, in particular away from home.
In a combined 125 Premier League games away at United, Chelsea, Arsenal and Liverpool, Tottenham have managed nine wins. And while their record at Manchester City is healthy, it cannot disguise a pattern of mediocrity against the top clubs.
There are encouraging signs that Postecoglou's expansive style is allowing Tottenham to go toe-to-toe with the title contenders, landing home wins against Liverpool and Manchester United this season and away draws at City and Arsenal.
Victory at United on Sunday, which would complete a first Tottenham double over the Reds for 25 years, would be the kind of statement victory to fuel title talk.
"I always feel I wasn't there so I don't know the reasons or whether there was something endemic in the club that didn't allow that," Postecoglou said when asked about Tottenham's struggles at the top clubs.
"I just tackle from when I get into a club, from there onwards. I think it is important how you perform in those games because if you want to be successful you need to be able to perform in those big games, particularly away from home."
Postecoglou's only loss to a top-six rival this season was the 4-1 home defeat by Chelsea which initiated a slump after a sparkling start to the campaign, although even in that game there were mitigating circumstances with Tottenham finishing the game with nine men and several injuries.
"We've done okay in those games (this season) not just results but performance-wise," he said. "I don't think we've walked away from any of those games and thought there was a massive gap between us and them.
"That is important and Old Trafford is another place where you know the atmosphere is going to be a great challenge for us. Home comforts are great, and we have a great crowd behind us, but if you can do it away from home in adversity I think it accelerates your growth."
