Pizarro has struggled to make an impact at Stamford Bridge since arriving from Bayern Munich on a free transfer and reports have claimed he could be heading to Argentina.
However, the player's agent Carlos Delgado has dismissed the rumours and says his client is happy with the Blues.
"Someone was bored and released that crazy news. Not only because River can't afford Claudio's contract but also because he is not interested in South America at all," Delgado told Radio Programas Peru.
"He has a contract with Chelsea and wants to play in Europe. This idea is as crazy as Universitario or Alianza signing (Hernan) Crespo."