|Date of birth||6 August 1996|
|Ternana (on loan from Sampdoria)|
|Amici di Mugnano|
|2016–||→ Ternana (loan)||1||(0)|
|* Senior club appearances and goals counted for the domestic league only and correct as of 5 September 2016.
‡ National team caps and goals correct as of 17 November 2015
Palumbo started his career at Amici di Mugnano youth academy. Palumbo and teammate Simone Russini were signed by Umbrian side Ternana in 2011. Palumbo made his professional debut in the first match of Ternana in the second round of 2014–15 Coppa Italia. He also played 12 times in 2014–15 Serie B season.
Palumbo received his first Italy U-20 team call-up in November 2015, replacing midfielders Lorenzo Pellegrini and Luca Mazzitelli who injured, Alberto Grassi who left for the U21 team. Palumbo was an unused bench against Germany on 12 November.
On 13 November Mazzitelli was returned from injury, but Alberigo Evani the coach still kept Palumbo in the squad, as well as adding Leonardo Capezzi to the call-up. On 17 November Palumbo was featured as a bench warmer again.
- "Comunicato Ufficiale (C.U.) N°24 (2009–10)" (Microsoft Word). Settore Giovanile Scolastico (SGS) Comitato Regionale Campania (in Italian). Federazione Italiana Giuoco Calcio (FIGC). 17 December 2009. Retrieved 16 November 2015.
- "Storie dal Sud: Simone Russini, dalla bocciatura del Napoli alla Ternana" (in Italian). la Giovane Italia. 30 September 2014. Retrieved 4 November 2015.
- "Torneo Quattro Nazioni: convocati 22 Azzurrini per la trasferta in Germania" (in Italian). FIGC. 5 November 2015. Retrieved 16 November 2015.
- "Torneo 'Quattro Nazioni': Azzurrini in Germania a caccia della prima vittoria" (in Italian). FIGC. 11 November 2015. Retrieved 16 November 2015.
- "15° TORNEO "QUATTRO NAZIONI" - Germania U20 vs Italia U20 0-2" (in Italian). Tutto Nazionali. 12 November 2015. Retrieved 16 November 2015.
- "Under 20. Torneo 'Quattro Nazioni': i convocati per la gara con la Svizzera" (in Italian). FIGC. 13 November 2015. Retrieved 16 November 2015.