After Brazilian Filipe Luis – who, according to media reports, is close to signing with Monaco – turned down the job, Bayer Leverkusen are, according to Sky, also said to be "pushing" for the appointment of Iraola and are "hoping for a quick agreement".
Oliver Glasner, who won the Conference League title with Crystal Palace on Wednesday, is also reportedly a candidate for the Leverkusen job.
Successful spell in the Premier League
Iraola – like Bayer’s title-winning coach Xabi Alonso, a Basque – set a new points record with Bournemouth in each of his three years at the club and recently went 18 Premier League matches unbeaten.
Bournemouth narrowly missed out on Champions League qualification, finishing sixth in the table. Iraola had already announced his departure back in April. Former Borussia Dortmund and RB Leipzig coach Marco Rose will take over from the Spaniard.
In Leverkusen, Hjulmand – who took charge after the second matchday of last season – is set to leave following a poor second half of the campaign and a sixth-place finish.