Pellegrini began with Estudiantes, who signed him from CRIM de Magdalena.[3][4][5] He was moved into the senior squad under manager Leandro Benítez during 2018–19, who selected him for his professional debut in a Copa Argentina tie with Central Córdoba on 24 July 2018.[1][6] After featuring in the 2018 Copa Libertadores versus Grêmio, Pellegrini made his first appearance in the Primera División on 12 August during a defeat to Godoy Cruz.[1][7] In his next match a week later, also in the league, he scored the first senior goal in a 2–0 victory over Boca Juniors.[1] Overall, Pellegrini ended his first campaign with four goals in twenty-three fixtures.[1]
Inter Miami
On 23 July 2019, Pellegrini agreed a transfer to Major League Soccer's Inter Miami,[8] and he was immediately loaned back to Estudiantes until January 2020.[9] The transfer fee was reported to be "between $6 million and $9 million."[10]
On 16 April 2021, Inter Miami removed Pellegrini from their roster to meet MLS requirements.[11] He was loaned to Fort Lauderdale CF, Inter Miami's USL League One affiliate.[12]
On 2 August 2021, Inter Miami loaned Pellegrini to his former club Estudiantes until June 2022 with an option to buy.[13] Estudiantes did not exercise their purchase option at the end of the loan, however, and Inter Miami subsequently waived Pellegrini so that he could join another MLS club on a free outside of the transfer window.[11]
New York City FC
On 19 August 2022, MLS club New York City FC claimed Pellegrini off waivers.[14] NYCFC announced on October 23, 2023, that the club declined Pellegrini's option, thus making him a free agent.
International career
Pellegrini was called up to train with the Argentina U17s in November 2016.[15] Two years later, in 2018, he was selected by the U20s.[16]