Reports reveal that Atletico Madrid are also keen on the 24-year-old, who could be sold this summer.
To re-sign Blues striker Romelu Lukaku, the Nerazzurri may need to raise necessary funds.
Chelsea could also replace Lukaku with Lautaro, but could face competition from PSG as they seek even more firepower up front.
The Argentina international scored 21 Serie A goals in 35 appearances in the just concluded season.