The Colombia international, who signed a one-year deal at Inter, won 11 trophies in eight years at Juventus -- the Nerazzurri's bitter rivals.
The 35-year-old Cuadrado has been involved in a number of incidents in matches between the two clubs, notably in April when the winger was sent off as the Italian Cup semifinal game ended in a scuffle. He was later banned for three matches.
As news of the potential signing of Cuadrado emerged, Inter fans protested outside the club's headquarters. They also unfurled a banner on Wednesday after the player arrived for his medical examination.
It read: "Until today you have done everything to make yourself hated, if that's not what you want it's up to you to show it."
Cuadrado has made 115 appearances for Colombia, with only David Ospina having featured in more matches.