Geelong superstar is edging towards an AFL return from the hamstring injury which has sidelined him since round three.
The Cats are still refusing to put a definitive time frame on the two-time Brownlow Medal winner's comeback but they issued a positive progress report on Wednesday.
"Gary's going well ... (he) ran again today and his running sessions have been completed pretty well," club physiotherapist Mark Young said.
"He'll join in football later this week and from there he shouldn't be too far away."
The 33-year-old injured his hamstring in the final quarter of the round three clash against West Coast.
It followed a similar injury which slowed him in the latter stages of the pre-season.
The 2-2 Cats have struggled with a lengthy injury list at the start of the season.
Cory Gregson suffered a foot sprain in Sunday's big win over St Kilda but the news actually came as a relief given he missed all of the 2017 with a foot issue.
While that diagnosis was a positive, the club revealed luckless defender Lachie Henderson underwent another bout of knee surgery on Tuesday.
It was Henderson's third operation on his right knee since the end of last season and there is no definitive time line for his return.
Key defender Harry Taylor remains out indefinitely with a foot injury.
Nakia Cockatoo (knee), Cam Guthrie (ankle) and Lincoln McCarthy (quad) are among the other players currently unavailable.
