Kakuta, 23, moved to Stamford Bridge from Lens in 2007 and was on loan at Rayo Vallecano last season, where he played 35 games.
The Frenchman played 16 times for the Blues, but spent time on loan at six different clubs.
In September 2009, Chelsea were barred from signing new players after being found guilty of inducing Kakuta to break his contract with Lens.
The ban was lifted by a court in February 2010 after the two clubs reached an agreement on his signing.
It is thought Sevilla have had to pay a fee for Kakuta because he is under 24.
In October 2014, failed footballer Medi Abalimba was sentenced to four years in prison after masquerading as Kakuta.
Manchester Crown Court heard Abalimba went on a £20,000 shopping spree at Selfridges, stayed at top hotels and even hired a helicopter.
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City are four points above the Premier League relegation zone and they want to sign a striker in January.
Paloschi, 26, has scored eight goals in 21 league games for Chievo this season.
Starting his career at AC Milan, the Italian also played for Parma and Genoa. He joined Chievo in 2011 and has scored 42 goals in 144 Serie A appearances.
Paloschi has represented Italy at Under-21 level, scoring in their 2-1 defeat to Wales at Swansea's Liberty Stadium in 2009.
He lined up alongside the likes of Milan and former Liverpool forward Mario Balotelli in a game won by Aaron Ramsey's spectacular strike.
Paloschi could now be about to link up with compatriot Francesco Guidolin, who was appointed Swansea's head coach earlier this month.
Former Udinese manager Guidolin guided the Swans to a 2-1 win at Everton in his first game in charge, the Welsh club securing back-to-back victories for the first time this season having previously beaten Watford.
Despite the encouraging start to Guidolin's reign, Swansea are still 15th in the Premier League table, with only bottom side Aston Villa scoring fewer goals so far in this campaign.

Karl Stefanovic wore the outfit to make a point about the sexism he said his female colleagues faced.
Nobody noticed he was wearing the same blue outfit, but he said his co-presenters would never have got away with it.
The profits will go to the charity White Ribbon, which campaigns to end violence against women.
He sold it on Ebay with the warning that "it's a little bit stanky (sic)" and added it "may need dry cleaning ASAP".
47 people bid for the suit and the lucky winner will get free delivery, meaning they should have cash spare to give it a good clean.
It was sold by the TV channel Karl works for with this description:
"Karl Stefanovic wore this stunning navy Burberry suit on The TODAY Show for one whole year to make a point about sexism. You have the chance at purchasing this suit for yourself, imagine how good you'd look in it! Super comfy, super stylish, super cool".
The 40-year-old, who has been a presenter and reporter for nearly two decades, has also participated in a variety of celebrity game shows in Australia, including Dancing on Ice and Hole in the Wall.
When he revealed that he wore the same outfit for a year he told The Age newspaper that his co-host, Lisa Wilkinson regularly gets messages from viewers and comments in the press about her fashion choices.
"Women are judged much more harshly and keenly for what they do, what they say and what they wear," said Stefanovic.
"I'm judged on my interviews, my appalling sense of humour - on how I do my job, basically. Whereas women are quite often judged on what they're wearing or how their hair is."
He started his experiment by wearing the suit two days in a row, without a comment. He then carried on for days and then months when he realised no-one was noticing.
"Only Lisa and [Today team member Sylvia Jeffreys] know about the suit. They often remark that it's getting a bit stinky," said Stefanovic.
"I'm hoping to get it into the dry cleaners at the end of the year."
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Chelsea's out-of-contract winger Gael Kakuta has joined La Liga side Sevilla.
[NEXT_CONCEPT]
Swansea City are in talks with Chievo about signing striker Alberto Paloschi for a fee of around £8m.
[NEXT_CONCEPT]
An Australian TV presenter has sold a suit he wore every day for a year for A$6500 (£3,500).