The Seagulls are eyeing a new striker this summer, and they have been linked with multiple names including Edouard.
It is now reported that they are in talks with the Hoops to land the Frenchman, who recently entered the final year of his contract.
Brighton are aiming to reach a transfer agreement by next week.
Brighton recently received £50 million from the sale of Ben White to Arsenal.
They have yet to make any signings from the funds received, and it could soon happen.
Potter has already ruled out the purchase of a new central defender this summer.
The focus could lie on pursuing a striker that can improve their scoring prospects.
The club created plenty of chances last term but were made to rue their poor finishing.
Danny Welbeck showed promise towards the end of the campaign to earn a new deal.
Neal Maupay is also in the ranks, but Potter may want more competition for places.
He went with a front two towards the end of the campaign with reasonable success.
Edouard, who bagged 22 goals and six assists last term, would be a quality signing.
He could be available for a reduced fee with his contract expiring in June next year.
Brighton also have an interest in Darwin Nunez, who is currently with Benfica.
However, a deal seems unlikely, with Benfica demanding as much as £38.4m.
Edouard could relish the prospect of testing himself in the Premier League.
The 23-year-old was heavily linked with Leicester City before they signed Patson Daka.
He would face a stern test of his credentials with a more physical and tougher challenge.
Stats from Transfermarkt.com