On 26 July 2019, Saveljich agreed to a permanent four-year deal with Rayo Vallecano, freshly relegated to the second division.

On 4 August 2017, after contributing sporadically to the Valencian club’s promotion to La Liga, Saveljich was loaned to Albacete Balompié in the second level, for one year. On 31 August 2018, he returned to Almería on loan for the 2018–19 campaign.

On 24 January 2016 Saveljich moved abroad, signing a six-month loan deal with Segunda División side UD Almería. On 18 August, he signed a permanent four-year deal with fellow league team Levante UD.

In January 2015 Saveljich was loaned to fellow top tier club Defensa y Justicia, until the end of the year. He appeared in 24 matches, scoring once, as his side avoided relegation.

Saveljich has obtained Montenegrin nationality in 2015. He was called up for international matches of Montenegro versus Denmark and Sweden in June 2015, both of which he entered as a substitute player. In Euro 2016 qualifying match against Russia, he was in starting line-up. Under Ljubiša Tumbaković, the new head coach of Montenegro national team, he played in friendly match against Greece.

Saveljich scored his first professional goal on 1 April 2014, in a 3–3 home draw against Estudiantes. He was also a part of the squad which was crowned champions in that year, but as a backup.

Born in Tandil, Buenos Aires Province, Argentina, Saveljich joined Racing Club’s youth setup in 2006, aged 15. On 23 June 2012 he made his first team – and Primera División – debut, in a 1–2 away loss against Vélez Sársfield.

Esteban Ariel Saveljich (Montenegrin: Естебан Савељић ; born 20 May 1991), also known as Esteban Saveljić, is an Argentine-Montenegrin footballer who plays for Spanish club Rayo Vallecano and Montenegro national team as a central defender.