The Italian champions beat Porto to reach the last eight, while the Foxes also progressed by overcoming Sevilla.
The Italy captain, 39, said: “Who do I prefer not to play? Leicester.
“They are a dangerous and passionate team who can cause trouble for opponents who take the initiative. We would have everything to lose.”
Real Madrid, who have won Europe’s premier knockout tournament a record 11 times and five-times winners Barcelona and Bayern Munich are among the sides already through to the last eight.
English champions Leicester reached the last eight in their maiden Champions League campaign with a 2-0 home victory over Spanish title hopefuls Sevilla to go through 3-2 on aggregate.
Juventus, who are two-time European champions, managed a routine 1-0 home win against Portuguese leaders Porto to complete a 3-0 aggregate victory.
They are widely ranked as fourth favourites to win the Champions League by many bookmakers, who also make Leicester the rank outsiders.