While Michael Carrick, who has a deal to June, is under consideration, the board is also considering alternatives, with Iraola now being discussed, says the i Paper.
The Spaniard is also a target for Tottenham, which intend to hire a long-term manager at the end of the season. Caretaker Igor Tudor will be moved on - potentially before the end of the campaign.
Crystal Palace are also watching Iraola's situation, viewing him as a direct replacement for departing manager Oliver Glasner.
Meanwhile, Bournemouth aim to open new contract talks with Iraola during this month's international break.
While his head will be turned by rival interest, Cherries management will highlight the demise of Thomas Frank at Tottenham after leaving the stability of his position at Brentford last summer.