The reports claim Arsenal boss Unai Emery is interested in signing the central defender.
The pair previously worked together when the Spaniard was in charge of PSG before he replaced Arsene Wenger at the Emirates.
Kimpembe was a key player for the French giants last season, making 36 appearances in all competitions.
But the possible arrival of De Ligt could tempt PSG into parting ways with the France international.
However a major sticking point for any deal would be Arsenal’s transfer budget.
Arsenal boss Unai Emery wants PSG star Presnel Kimpembe (Image: GETTY)
Presnel Kimpembe is said to have a frosty relationship with PSG team-mate Neymar (Image: GETTY)
Arsenal: Kieran Tierney would ‘fit the bill’ claims fan
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It is believed the Gunners will only have around £45million to spend this summer after failing to qualify for the Champions League.
Arsenal have also been linked with Sampdoria defender Joachim Andersen and Saint-Etienne starlet William Saliba.
In addition to a centre-back the Gunners are looking to replace Aaron Ramsey who has left for Juventus and strengthen their backline with new full-backs.
Arsenal are also interested in signing Celtic left-back Kieran Tierney and are prepared to offer the Scottish champions Carl Jenkinson as part of a swap deal.
Express Sport understands Celtic want around £25m for Tierney, which would make a huge dent in Emery’s transfer budget.