The Frenchman took just 53 minutes to net the treble as the champions ran out 5-1 winners on the opening weekend.
Edouard is attracting interest from across Europe following his Scottish exploits in recent seasons.
Arsenal continue to be tentatively linked with the 22-year-old, who joined Celtic in 2017 after leaving Ligue 1 winners PSG.
And with Pierre-Emerick Aubameyang potentially on his way out of the club, Gunners supporters want to see Edouard in as his replacement in the near future.
"Edouard is definitely getting a move to the prem next season. As much as I love Laca I’d love to see him at Arsenal," one wrote.
"Bloody hell. Edouard just got a hat trick so quickly! C'mon," one said.
"@Arsenal, get on this transfer!" a third added.
"Edouard come to Arsenal," demanded a fourth.
"Arsenal should be looking at Edouard this when Auba’s time comes to an end," one said.
"Odsonne Edouard is a dangerous player and a natural finisher, Arsenal really need to look at buying him, he won't cost too much seeing as he's playing in Scotland and he'd love to join Tierney in London..." wrote another.
Celtic fans are desperate to keep Edouard at Parkhead for the foreseeable.
But Neil Lennon admits his side know the day will come when he departs.
“It’s as you were with the contract talks. There’s been no further movement on it. Whether it’s Edouard or any other player, in previous years we sold guys like Moussa Dembele and Kieran Tierney, it’s not something we won’t be prepared for," he said.
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“It’s not something we want, but there may be intense speculation surrounding a number of our players, so we have to plan ahead and that’s what we do.
“It’s like a circular motion. We have got to keep the wheels moving and be prepared for any eventuality when the market opens.
"It's going to be a long transfer window. There will be pros and cons. Sometimes it can work in your favour, other times to your detriment. We’ll have to adapt to that as well and be patient.”