PSG made a cheeky attempt to prise Diego Costa away from Chelsea last month.
France Football says during deadline day negotiations over David Luiz's sale to Chelsea, PSG asked about taking Costa in part exchange.
PSG had hoped to sign the Spain striker as a replacement for Manchester United's Zlatan Ibrahimovic.
Chelsea management were open to the idea, but eventually the proposal was vetoed by manager Antonio Conte.
Costa, despite last season's problems, has kicked off this campaign in impressive goalscoring fashion.