The Sunday Express says they have completed the signing of £32million Leicester midfielder N'Golo Kante and are now planning a second raid on the Premier League champions for winger Mahrez.
The Algerian international is on the verge of turning down a new Foxes contract worth £100,000 a week.
And that will alert a number of Europe's biggest clubs tracking the 25-year-old, who signed for £350,000 from Le Havre in 2014.
Conte has made no secret of his desire to sign a goalscorer and PFA Player of the Year Mahrez, who hit 17 last season, fits the bill.