The 41-year-old Uruguayan international is believed to be amongst the leading candidates to become the new boss at The Liberty Stadium.
"I would really be interested in the job," Poyet told BBC Sport Wales.
"I would really like to go there, it would be a great opportunity."
Sheffield United player/coach Gary Speed and former Watford boss Aidy Boothroyd are also said to be on the shortlist for taking over the role made vacant by Roberto Martinez's departure to Wigan earlier this month.