Corentin Tolisso is a target of Chelsea this summer
Antonio Conte has longed for a box-to-box midfielder after attempting to sign Radja Nainggolan last year from Roma.
Tiemoue Bakayoko was believed to be the club's top target but there have been complications in the deal.
And with reports of Nemanja Matic on the verge of leaving for either Manchester United or Juventus, the Blues are keen to reinforce the middle of the park.
European football expert Sierra, who has more than 26,000 followers, tweeted that the club have made an official offer of £30.5m (€35m) for Tolisso after it emerged yesterday that Bayern Munich were also sniffing around the French star.
He wrote: “confirmed: #Chelsea has made an official offer of 35M€ to the #Lyon for the French midfielder Corentin Tolisso (22).”
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The 22-year-old has been in fine form for Lyon this season, scoring 14 goals and registering seven assists across all competitions.
The midfielder is believed to want a starting role wherever he goes as he seeks a place in France's World Cup squad next year.
Despite Bayern losing Xabi Alonso to retirement, their midfield options still boast the likes of Arturo Vidal, Thiago Alcantara and Renato Sanches.
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Tolisso has one cap for France, having made his debut in March this year.
There have also been reports of Bertrand Traore being loaned to Lyon as the Chelsea board cosy up to the French outfit.
Traore has been on loan at Ajax this season and played in Ajax's Europa League final 2-0 defeat to United.