Kakuta, who will turn 24 on Sunday, joined Chelsea from Lens aged 16 but struggled to break into the first team and was loaned out to clubs including Fulham, Bolton Wanderers, Dijon, Lazio and Rayo Vallecano.
Sevilla are hoping he can rediscover the form that earned him the player of the tournament award when he helped France win the Under-19 European Championship in 2010.
"Gael Kakuta will arrive in Seville on Thursday for a medical," Sevilla said on their website (www.sevillafc.es).
"If everything goes well Sevilla FC and Chelsea will sign the papers that seal the transfer," the La Liga club added.
Sevilla's second straight Europa League triumph at the end of last month earned them a place in the Champions League group stage for next season.
(Reporting by Iain Rogers, editing by Toby Davis)
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