Over the weekend, the Blues confirmed that they had secure the signature of Napoli centre-back Kalidou Koulibaly on a long-term contract.
However, head coach Thomas Tuchel has openly acknowledged that he is continuing to prioritise more defensive additions in order to replace the likes of Andreas Christensen and Antonio Rudiger.
At one stage, Manchester City's Nathan Ake appeared to be Tuchel's preferred option before it became clear that the Dutchman would be remaining at the Etihad Stadium.
Now, the West Londoners are seemingly deliberating over whether to make sustained bids to sign Kimpembe or Sevilla's Jules Kounde.
According to the Daily Mail, Chelsea have already made a £40m bid for the services of Kimpembe.
Speaking last week, new PSG head coach Christophe Galtier insisted that he did not know whether the France international would spend 2022-23 at Parc des Princes.
Galtier said: "I've read everything that has been said about Kimpembe. We even laughed about it together! I like him - he's a great centre-back but what will happen, I don't know."
Further reports have claimed that the 26-year-old will be allowed to decide his own future with PSG seemingly open to a sale for the right price.
The report claims that that the Ligue 1 champions are prepared to sell Kimpembe for a fee in the region of £42m, marginally above Chelsea's current proposal.
Although Kimpembe has just two years remaining on his contract, it has previously been suggested that his love of Paris may keen him in his homeland's capital.
Kimpembe has spent his entire career with PSG, making a total of 221 appearances for the club in all competitions.
The report adds that Chelsea have also resumed talks with Sevilla regarding the potential addition of Jules Kounde, who has a £69m release clause in his contract.
However, as it stands, Chelsea have shown no desire to meet that fee, leaving the relevant parties to try to negotiate a deal.