Reports earlier this week claimed the Blues were ready to smash their transfer record for the Italian side's star man Victor Osimhen after a start to the season full of missed chances.
Mauricio Pochettino's men are ninth in the Premier League goalscoring charts despite spending £1billion over the past 18 months.
So far £32million summer signing Nicolas Jackson has struggled in front of goal, while the Blues are still awaiting the return of Christopher Nkunku.
That has seen 24-year-old Osimhen singled-out after he led Napoli to their first Serie A title in 33 years last season as the league's top scorer.
Diego Maradona's old side have reportedly put a £120m price tag on their No.9, putting off suitors in the summer, but not Chelsea in January.
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However, the Blues' hopes of landing the marksman have now taken a big knock due to comments from Napoli president Aurelio De Laurentiis.
Asked about Osimhen's contract situation at an awards ceremony, he stated: "For Osimhen we are now at the signing stage which has been pending since the summer."
To add to De Laurentiis' confidence, Italian outlet Corriere dello Sport claim Osimhen's agent travelled with the team for their Champions League clash away to Real Madrid midweek.
There he was able to sit down with the club's hierarchy and discuss an extension, new salary and release clause for the Nigerian.
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