The Norwegian is rumoured to be interesting the likes of Besiktas, Sevilla and Celta Vigo.
Elyounoussi hasn’t had the happiest of times since signing for Southampton from FC Basel last summer for a reported £16.2m.
He made 19 appearances in all competitions for Saints last season, failing to register a goal or an assist in that time.
In reference to Elyounoussi’s future at Southampton, Hasenhuttl was quoted by Norwegian news outlet TV2 as saying the following:
“We want to give everyone the chance to play. If he doesn’t feel comfortable sitting on the bench, or maybe in the stands sometimes, he has goals other than us.
“Then we should find a solution. Normally, we tend to get it.”