The Sun is reporting that the Blues are interested in a potential swoop to sign the Brazilian midfielder in the summer transfer window.
The same article states that their Premier League rivals Everton and Tottenham Hotspur are also interested in the South American after his performances in the Champions League this term.
According to the same story, Spartak Moscow will demand at least £22m for Fernando, which some English clubs could be reluctant to meet.
Fernando has scored five goals and has made two assists in 25 appearances in the Russian Premier League this term.
The defensive midfielder scored one goal in six games in the Champions League. Spartak Moscow drew 1-1 with Liverpool FC in Russia before the Reds were 7-0 winners at Anfield in December.
Chelsea FC signed AS Monaco midfielder Tiemoue Bakayoko and Leicester City star Danny Drinkwater in the 2017 summer transfer window.
The duo have struggled to impress in the Blues team after Chelsea FC opted to sell Serbia international Nemanja Matic in a £40m deal to their bitter title rivals Manchester United last summer.
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