French outlet RTL, as quoted by Metro, is reporting that the Blues are hoping to conclude a deal to sign the 26-year-old as their first recruit of the summer transfer window.
Arsenal reportedly held talks over a deal to sign Seri last summer but a move failed to materialise for the midfielder.
Manchester United are also said to have shown an interest in signing the Nice midfielder this summer as Jose Mourinho looks to strengthen his squad ahead of next season.
According to the same story though, it is Chelsea FC who are leading the race to sign Seri this summer, despite the uncertainty about the managerial situation at Stamford Bridge.
Chelsea FC are yet to make any new signings this summer as they look to assemble a squad capable of winning the Premier League title next season.
It turned out to be a disappointing campaign for the Blues as they missed out on Champions League qualification due to their fifth-placed finish in the Premier League.
However, they did end the campaign on a high by beating Manchester United in the FA Cup final at Wembley last month.
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