The Colombia international managed to get his career back on track in Turin after an unsuccessful spell at Chelsea, and recently made his loan move to Juve permanent.
Cuadrado's exploits in Italy, where he has won back-to-back domestic doubles, saw him linked with a move back to London as Gunners boss Arsene Wenger looks to bolster his squad for another try at the Premier League title.
But Alessandro Lucci says his client's future is not up for discussion as the Serie A champions are not planning to sell the 29-year-old former Fiorentina star.
"Juan does not want to leave Juve and Juve do not want to sell him so there are no ongoing negotiations at the moment," Lucci told Gianluca Di Marzio.
"Nobody has neither contacted me nor Juventus and I am the only one in charge to talk about the future of Juan."