The Blues have been tracking Brighton and Republic of Ireland star Ferguson for some time.
They also have a good relationship with Brighton, having paid well for Marc Cucurella and Moises Caicedo from the Seagulls as well as manager Graham Potter and several backroom staff.
However, Ferguson only signed a new contract in November and Brighton believe he is worth more than the £115m British record fee they got for Caicedo.
It is also thought Ferguson is in no rush to leave.
Ferguson's impressive performances attracted interest from Manchester United last summer and also from Tottenham who were on the lookout for Harry Kane's replacement.
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Chelsea's search for a striker has seen them linked with Napoli's Victor Osimhen and Brentford's Ivan Toney.
Both signings would command a sizeable transfer fee and a wage in excess of £200,000-a-week.
However, a move for Ferguson would help Chelsea keep their wage structure intact whilst investing in a player with his best years ahead of him.
Despite another stuttering league campaign, Chelsea are likely to wait until the summer before addressing their need for a striker.
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Eight-goal marksman Nicolas Jackson has had to bear the brunt of the Blues' goalscoring expectation and will be expected to push on in the second half of the campaign.
But with that comes a pressure for tenth-placed Chelsea to climb the Premier League table and challenge for European qualification.
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A second consecutive failure to qualify for Europe could have financial consequences for Chelsea's summer transfer window.
It could also force the club to part with a number of their home-grown assets such as Conor Gallagher and Trevoh Chalobah to balance the books.
Both players have been linked with moves away from the club and another underwhelming season could force Chelsea's hand.