Iraola is expected to leave Rayo this summer.
Estadio Deportivo says the 40-year-old Spaniard has three main tracks - but that none of them are straightforward.
Leeds, who were looking for Iraola already earlier in the season, remain an option.
At the same time, much will depend on whether they manage to stay in the Premier League.
Further there is Sevilla, who earlier in the season had an agreement with Iraola to take over this summer.
But the hiring of José Luis Mendilibar and his success has complicated that possibility.
Finally, there is Villarreal, but even there coach Quique Setién has impressed since taking charge midseason.