The 28-year-old impressed David Moyes while the Sunderland manager was at Real Sociedad and the Scot is hoping to bring the player to the Stadium of Light.
Iborra has been at Sevilla for just over three seasons where he has played 131 times and scored 22 goals. He has also been part of Sevilla's three consecutive Europa League triumphs.
The Spaniard has been likened to Manchester United midfielder Marouane Fellaini and Moyes was said to be interested in signing the Belgian at the start of the summer, but Fellaini is now enjoying a run in United's first-team.
Sunderland have struggled at the start of this season, taking just one point from their first three league games.