The Mirror claim the experienced boss, who is currently leading Italy at Euro 2016, sought out the Spanish duo when their nations met during Euro 2016.
And it's suggested the incoming Blues chief told the pair that they are in his plans for next season.
Azpilicueta has been linked with a move away from Stamford Bridge.
The Mirror claim Barcelona, Athletic Bilbao,Manchester United and Bayern Munich are all potential suitors.
But Conte’s assurances have not put off Bilbao.
It's claimed the La Liga outfit are readying a £12m bid for the influential full back.
Winger Pedro revealed to beIN Sports earlier this month that he would like to return to Barcelona before the end of his career.
He also admitted to speaking with club president, Josep Maria Bartomeu, and refused to rule out a reunion at the Nou Camp.
However, Conte's intervention might have convinced the wide man to remain in west London.
He has only spent one season in the Premier League having switched from Barcelona for £21.4m in August.
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