The Spain international has not been a regular at Stamford Bridge following the return of Jose Mourinho as manager.
PSG failed to sign the Spaniard in the summer and The People reports that the French giants have made signing Mata a transfer priority in January.
Mata has been named as Chelsea player of the season for the past two years.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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