It has been heavily anticipated that the 26-year-old will leave Grand Stade Lille Metropole this summer, with a number of club's vying for the player's signature.
Gunners boss Arsene Wenger had been credited with an interest in bringing the France international to the Emirates Stadium, but is now turning attention to alternative targets after news broke of Payet's intention to stay in Ligue 1.
Marseille president Vincent Labrune held talks with his opposite number Michel Seydoux on Tuesday evening, and is understood to have thrashed out an £8.5million deal plus potential add-ons - which is an initial £1million more than the price Lille paid for Payet two years ago.
Arsenal forward Gervinho was also mooted as a potential transfer target for Marseille in recent weeks, but Elie Baup is likely to end his interest in the Ivorian once the capture of Payet is completed.
The two French clubs have been at loggerheads over the player's valuation for some time, but now look to have finally agreed on a price to make the move happen.