The former Reds and Valencia defender was brought to Anfield last year by Benitez and is happy with his growing education.
On his own managerial ambitions, Pellegrino told liverpoolfc.tv: "I don't know. In football our life changes every single week. We don't know what will happen in the future so I don't like to think about it. I enjoy my job right now, try to improve every single day and think about the best for the team and club.
"I have learned a lot in this past year from Rafa. I worked with him as a player too. The mood now among the staff here is very good."