The 32-year-old is contracted to the Giants for 2027, but wants a move back to his home state after two seasons in NSW.
It comes amid ongoing uncertainty around the playing futures of GWS captain Toby Greene and key forward Jesse Hogan.
"I'll probably most likely go back to Melbourne, just for family reasons," Stringer told reporters on Thursday.
"My dad's been sick throughout this whole year and being away from my two girls back in Melbourne's been challenging.
"So most likely, it's probably my last game for the Giants (against Adelaide on Saturday night)."
Stringer has played 37 games for GWS, including a career-best haul of seven goals that inspired an upset win over ladder-leaders Fremantle last month.
The Giants' clash with the finals-bound Crows at Adelaide Oval will be Stringer's 250th AFL appearance.
He played five seasons with the Western Bulldogs, featuring in the drought-breaking 2016 premiership, before spending seven years at Essendon.
"Definitely feel like I've got quite a few more years left," Stringer said.
"But I'll just get through this weekend, reassess, spend some time with the family, go back home and work it out from there.
"There's been no decision or anything like that. I'm just looking forward to finishing it off here, enjoying more time with my teammates who I absolutely love, and go from there."
Hogan has a finger injury and has not played for GWS since a loss to Carlton in June.
The 31-year-old, who started his AFL career with Melbourne and spent two seasons with Fremantle, has been linked to Gold Coast and Collingwood.
GWS games record holder Greene is also considering ending his decorated career in Victoria after 15 seasons with the Giants.
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