Ruled out of the season start with a calf strain, the gun midfielder is not expected to feature until after the Giants' round-two bye.
Green suffered the injury during an intra-club match simulation four weeks out from their March 9 hit-out against Collingwood at Engie Stadium.
Should he suffer setbacks, the 24-year-old could have more time out than the original prognosis of four to six weeks.
That is an outcome Green is refusing to entertain.
"If there's any opportunity for me to get back before (the round-two bye), I'm not going to be leaving any stone unturned," Green said on Thursday.
"It's coming along really well.
"It's not ideal and it's frustrating, but it could certainly be worse."
One of the most important players in the Giants engine room, Green will be sorely missed against Collingwood.
He averaged 30.8 touches and 6.2 clearances last season to lead the league with the most disposals (770).
The Giants will at least welcome back veteran midfielder Stephen Coniglio and Sam Taylor for their final pre-season match against Carlton at Manuka Oval on Friday.
Coniglio had been rested for last week's simulation against Sydney after undergoing facial surgery and a shoulder reconstruction, while Taylor was out with concussion.
But recruit Jake Stringer has again been ruled out with illness, having also sat out against the Swans.
Second-year player Phoenix Gothard, in the frame for an opening-round debut, joins Stringer on the sidelines with a sprained ankle.
Green admits their 57-point simulation loss to Sydney had left his side with much to think about.
"We haven't done as much match sim as some other sides so we've looked a little bit rusty in some of our hit-outs, but that's to be expected," Green said.
"We talk about trying to play our best footy towards the back end of the year, and so we understand that that's going to come with a little bit of rust this time of year.
"With unfortunate things like injuries and suspension and stuff like that, it gives other guys who are looking to cement themselves opportunities."
Cody Angove will be out to impress against the Blues in a bid to secure his debut in opening round.
The 18-year-old, drafted with pick No.24 last year, stood out on the wing against the Swans with two goals.
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