According to the 'Daily Mail', the Blues are keeping an eye on the 20-year-old defender because they are unhappy with the performances of summer signing Antonio Rudiger, who joined from Roma for a fee of around £29m.
Rudiger has struggled to adapt to life in the Premier League and has endured an inconsistent and frustrating start to his Chelsea career.
Meanwhile, Diakhaby, who is 6ft 4in, has emerged as one of the best youngsters in Ligue 1 since making his debut in September 2016. He has since made 40 appearances for Lyon in all competitions, playing six times so far this season, scoring one goal.
He is contracted at Lyon until 2022 and is a product of the club's famed youth academy and he has made five appearances for France U21s. The young defender has gained a reputation as a composed defender and is also a threat from set-pieces.
Antonio Conte is considering a move for the young Frenchman as he looks to bolster his defensive options at Chelsea, but he is likely to face stiff competition from current Premier League leaders Manchester City.