The Bianconeri midfielder was set to move to Spanish club Valencia, but the two clubs were not able to find an agreement over the fee.
Udinese president Vittorio Pozzo preferred to loan Pizarro to the Chilean club until next summer.
Last week the player revealed he does not like Udinese coach Luigi De Canio and Pizarro could be sold in the next months.
Meanwhile Pozzo has confirmed that he is not trying to Parma striker Marcio Amoroso back to the club.
The president also confirmed that the club will not sell Massimo Margiotta and Vincenzo Iaquinta, both chased by Serie A rivals Brescia.
