Griffen, who has been dealing with tightness in his back, was restricted to walking laps at training on Tuesday morning.
McCartney said Griffen would have the opportunity to prove his fitness this week.
"Ryan's fitness is gaining daily momentum. He's doing more and more training, and more importantly he's recovering from that training and he's very, very close to playing," McCartney said at the Whitten Oval on Tuesday morning.
When asked to put a percentage on Griffen's chances of leading the team out onto Patersons Stadium against the Eagles, McCartney was tight-lipped, saying only, "He's very, very close to playing."
Griffen did not play in any of the Bulldogs' NAB Challenge hit-outs, nor did he participate in the club's practice match against Carlton or last Thursday night's intra-club match.
Veteran defender Robert Murphy, who has recovered from an elbow injury, will mark his return by playing his 250th game for the Bulldogs.
Murphy managed to avoid surgery that would have forced him to miss the start of the season.
"He's just a great man to have in your club. He's just a brilliant person to coach and if you're a young player in the club, then you're quite blessed to have people of his calibre around you to learn from and want to emulate," McCartney said.
"We're thrilled to bits that he's made it back and dodged a bit of a bullet with the injury, so it'll be nice to have him out there."
One of those young players who can count Murphy as a mentor is second-year midfielder Jack Macrae, and McCartney said he was ready to take the next step.
Macrae, 19, averaged 29 disposals during the Bulldogs' two NAB Challenge games against St Kilda and Fremantle.
"He is (ready to take step up), but he's still a young boy. He's just learning to cement his position as a winger and he spends a little bit of time around the ball," McCartney said.
"He's a high talent with still lots to work on and he's making really good progressions."
McCartney expects the Eagles to pose a tough challenge for his young side.
"They (the Eagles) were on track in the middle of last year, but I think it got lost that they had so many injuries," he said.
"They've clearly ticked all the boxes in the pre-season and they'll be hard work, but we're really looking forward to getting on a plane and going to play a good game of footy."
