Pedzisa mutsara unotevera: An Algeria international, Slimani akaita mutambo wake wepasi rose mu2012 uye akatamba muAfrica Cup of Nations mu2013, 2015 na2017, uye aive chikamu chechikwata cheAlgeria chakakunda mukombe weAfrica Cup mu2013.
Makwikwi a2019. Aivewo chikamu chechikwata cheAlgeria pa2014 FIFA World Cup, kwaakapedza semutambi wepamusoro wechikwata aine zvibodzwa zviviri. Kubva munaKurume 2021, akahwina pamusoro pemakumi manomwe emakwikwi epasi rese uye akarova zvibodzwa makumi matatu nezvitatu, zvichimuita wechipiri weAlgeria wepamusoro-soro zvibodzwa.