Tuttosport says Inter have sparked a four-way battle to sign Pogba in the summer.
Real Madrid boss Zinedine Zidane is very keen to lure the British record signing to the Bernabeu.
A return to Juventus, where he spent four years between 2012 and 2016, is another possibility.
Pogba grew up in the suburb of Lagny-sur-Marne in eastern Paris so would no doubt relish the chance to represent his hometown club.
But Inter Milan are also hoping to seal a deal for Pogba.