The Blues have already been proactive in their efforts to sign new players this summer, with Christopher Nkunku and Nicolas Jackson being tapped to bolster their attack.
Mauricio Pochettino is seemingly still in the market for a new centre-back, central midfielder and a player who can be deployed in a number of roles in the final third.
While other players have been linked with a move to Stamford Bridge in recent weeks, speculation regarding a potential approach for Mbappe is not going away.
With the French foreigner not appearing to have any interest in a renewal at the Parc des Princes, PSG are eager to find a client for his services, which has been unlikely lately.
No European club is willing to pay big money for a player who PSG feel is keen to sign for Real Madrid in 12 months time, resulting in a loan exit becoming a realistic possibility.
Earlier this week, Liverpool manager Jurgen Klopp played down the possibility of Mbappe moving to Anfield on those terms, but Chelsea co-owner Todd Boehly reportedly held talks with PSG president Nasser Al-Khelaifi.
While it is unclear that progress has been made in those talks, Sport claims that the Premier League side are active in the race to sign Mbappe.
The report claims that while Mbappe has no interest in signing for Chelsea on a permanent basis, he is willing to settle for a one-year loan in west London.
Mbappe is keen to stay in his own future, indicating that he is willing to stay on the outer edge of Luis Enrique’s team if he doesn’t get the desired move in due course.
PSG have already excluded Mbappe from their plans for the new crusade and are reportedly looking for a replacement who movement expert Fabrizio Romano believes could be Benfica’s Goncalo Ramos.
In addition, Sport claims that a loan would not be suitable for either PSG or Chelsea, but it would be possible to find a solution.
Real Madrid have reportedly not taken any steps to try and sign Mbappe this summer, aware that their long-term target is a free agent at the end of June.