The centriole undergoes duplication during:

Centrioles undergo duplication during the S phase of the interphase and begin to move towards the opposite pole of the cell during the prophase stage of mitosis.

S phase is the period of DNA synthesis during which the cell replicates its genetic content; a normal diploid somatic cell with a 2c complement of DNA at the beginning of the S phase acquires a 4c complement of DNA at its end.