He is a product of Roma youth teams and started appearing for their Under-19 squad in the 2016–17 season.[1]
He first appeared for Roma's senior squad on 14 July 2018 in a pre-season friendly against Latina.[2] He was called up to the senior squad on several occasions in the 2018–19 Serie A seasons, but did not make any appearances.
Loan to Vibonese
On 18 July 2019, Greco was loaned to Serie C club Vibonese on a season-long loan deal.[3] He made his professional Serie C debut for Vibonese on 25 August 2019 in a season-starting game, a 1–0 away defeat against Monopoli.[4] He established himself as Vibonese first-choice goalkeeper early in the season. Three weeks later, on 15 September, Greco kept his first clean sheet for the club, a 3–0 home win over Rende.[5] Greco ended his season-long loan to Vibonese with 20 appearances, 30 goals conceded and only 1 clean sheet and he also remaining an unused substitute for 9 other league matches.[6]
Loan to Pro Patria
On 12 August 2020, Greco was signed by Serie C club Pro Patria on a season-long loan deal.[7] On 27 September he made his debut for the club and he also kept his first clean sheet in a 0–0 away draw against Carrarese.[8] Ten days later, on 7 October, he kept his second clean sheet in a 1–0 away win over Olbia, and on 10 October, his third in a 0–0 home draw against Pistoiese.[9][10] Greco helped the club to reach the play-off, however the club lost 3–1 against Juventus U23 in the first round and he ended his season-long loan with 35 appearances, 27 goals conceded and 18 clean sheets.[6]
He was first called up to represent his country in 2014 with the Under-15 squad.[12]
He later appeared for Under-16, Under-17 and Under-18 squads, all in friendlies. He was not selected for the 2016 UEFA European Under-17 Championship squad despite receiving call-ups at qualification stage.
