Hogan is among five key Giants pressing to play in Saturday afternoon's elimination final in Sydney.
The key forward hasn't played since round 22 because of a lingering foot injury.
"He's good to go," Greene said on Tuesday.
"He'll be there Saturday.
"He'll do whatever he has to do on Thursday (to prove his fitness).
"He's turned it around pretty quickly because we weren't sure if we were gonna get him for the first final and if we win and then go from there, how many finals.
"So it's great to have him, we know what he can bring. I'm sure he's gonna be hard to play on, on the weekend."
Coach Adam Kingsley on Monday night said Hogan will decide after Thursday training whether he is fit enough to face the Hawks.
"He is in a position now, should he get through the week, where he's comfortable that he can get through a game - and perform, most importantly," Kingsley told Fox Footy's AFL 360 on Monday night.
"And if that's the case, then we will pick him.
"But we kind of won't know that until he runs around on Thursday, has a decent session, and makes the call himself.
"We trust him. He knows his body extremely well, he knows whether he's capable of getting through a game or, more importantly, capable of performing in a game.
"He will make a really important call, a solid call, that is team before him, and we will trust him whichever way he says."
Midfielder Josh Kelly (calf), defender Jack Buckley (calf), Jake Stringer (hamstring) and veteran Stephen Coniglio - who will exit concussion protocols on Friday - also face fitness tests.
"Then as a match committee we have to put our heads together and work out, is there any compromise to our team if we pick all five?" Kingsley said.
Greene said the Giants needed players capable of going 120 minutes, but backed the coach to make the right call.
Buckley sat out Tuesday's training while a frustrated Brent Daniels left the track early, casting doubt over his availability.
"He's still a big chance to play. I'm sure we'll find out a bit more Thursday, that'll be a bit more of a test," Greene said.
"He's always a little bit frustrated, 'Binga'.
"He wants to be out there and do as much as he can every session, so he'll be fine. He'll just work through it Thursday and go from there."
The Giants finished fifth and are determined to go deep into September.
"We don't want to just play finals, we want to win them," Greene said.
9°C