The lock has been sacked by Racing 92 for his late return to the Paris club after playing for Fiji at the Rugby World Cup in Japan.
Nakarawa was key to Warriors' 2015 PRO12 title win during a three-year stint before joining Racing in 2016.
The news of Nakarawa's availability will alert clubs all over Europe but Glasgow head coach Dave Rennie hopes that the player's continuing friendship with old team-mates such as Ryan Wilson will tip the balance in the Warriors' favour.
"He's really tight with a lot of these boys," the head coach said. "I know Wilson's in constant contact with him. Yeah, he's a fan favourite, he loved it here, the boys loved him, so if we can make it happen that would be brilliant."
Asked if an approach would be made to Nakarawa or his representative, Rennie went on: "Yes, there will be. Obviously it's only become official today. Like I say, there'll be a bit of follow-up now."