Gibson rolled his ankle against the Sydney Swans in round five, missing Saturday night's 35-point win over St Kilda.
The 28-year-old is hopeful of a return against the Demons.
"We've got our final training session on Thursday, so I'll have a run around then and hopefully play," Gibson told Triple M on Tuesday night.
Hawks football operations general manager Mark Evans told hawthornfc.com.au Gibson was "improving all the time".
"It's still only Tuesday, so we've got a bit of time left to see where he's at by the end of the week," Evans said.
Hawthorn will also hope Luke Hodge can recover from the battering his body took against the Saints.
The Hawks skipper had treatment on the sidelines after getting a heavy knock to his hip/back.
"He's a bit bruised from the game," Evans said.
"He had a couple of big collisions, but that's typical 'Hodgey'; I would think he'd be like that every second game.
"We're hopeful that he'll be OK by the end of the week."
Key defender Jarrad Boumann will spend at least two weeks recovering after having his appendix out on Monday.
Evans said the club thought the issue was unrelated to the cramps Boumann suffered during the match on Saturday night, which led to him being subbed off.
"He had some stomach pain on Sunday and reported it to the doctor, and after a bit more assessment they decided to take his appendix out," he said.
"We're anticipating he'll be out for two to three weeks."
Fellow backman Ben Stratton had a nasty head clash with Saint David Armitage, but was able to play on and is available for this week.
Stephen Gilham, on the comeback from a knee reconstruction, could come into the frame for his first senior match since round eight last year after playing well in Box Hill's win over Frankston last weekend.
"The last two games he's played at Box Hill he's gone well, so I'm sure he'll be pleased with that," Evans said.
Injury list
Max Bailey (wrist) - TBC
Jarrad Boumann (appendix) - 2-3 weeks
Xavier Ellis (calf) - 1-2 weeks
Josh Gibson (ankle) - testAlex Woodward (knee) - season
