Kondogbia has also been linked with clubs such as Real Madrid, Chelsea and Manchester United.
The Daily Mail reports that Arsenal hope they can agree a fee with Spanish side Sevilla before orther clubs make their moves.
The Gunners have also been linked with the likes of Newcastle keeper Tim Krul and Swansea defender Ashley Williams.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.