Graham injured his calf in the opening minutes of the match against the Kangaroos last week and had scans yesterday to determine the extent of the injury.
Coach Mark Thompson said the scans didn't reveal serious damage but conceded calf injuries could be difficult to overcome.
He is hopeful Graham will come up but the skipper will be rested from the Cats' regular training sessions this week.
``He won't be doing any of the skills and we'll give him a run on Saturday morning and make a decision before the reserves game,'' Thompson said at training last night.
``There was nothing in the scan, which is a good sign. But he did get a corky in the calf and when they're bad enough they can keep you out of the game.
``We'll wait until Saturday but we're confident he'll be right.''
Geelong's backline strength has been stretched by the injuries to Graham and Darren Milburn, with vice captain Brenton Sanderson still out for a couple of weeks.
``It's a bit of a worry losing Dasher (Milburn). He's been a good player all year and we really rely on him,'' Thompson said.
``He's an integral part of the backline and we'll miss him.''
But the good news for Geelong is that Jarad Rooke is expected back, although Thompson wasn't sure he'd walk straight into the seniors after more than a month on the sidelines.
``Jarad Rooke will probably play this week which will be a bonus,'' Thompson said.
``Whether he plays firsts or seconds I'm not too sure, it's too early to tell. He might be a bit green
``But he might also be worth the risk because he'd be an automatic replacement for Milburn.'' Thompson said veteran Tim McGrath, the backline general in the VFL side, is in the mix for to senior selection given the run of injuries to backline players. Mitchell White will also be considered after coming through a couple of VFL matches unscathed.