Poyet is reported to have met – and impressed – the Swansea board as they search for a replacement for Roberto Martinez.
The Uruguayan midfielder has been out of work since being dismissed along with Juande Ramos at Spurs and is thought to be keen to return to management with Swansea high on his list of preferences.
The Swans have said they are down to six candidates as they look to replace Martinez who was confirmed as Wigan manager earlier this week.
Speaking to BBC Sport, Poyet said "I would really be interested in the job
"I would really like to go there, it would be a great opportunity."
Swansea Chairman Huw Jenkins is also reported to have met with former Wales midfielder Gary Speed who is second favourite with the bookies to take the job.
This article first appeared on JACKARMY.net.