Rosenior lost his job with the London club on Wednesday, after a run of five defeats without scoring, the club’s worst scoreless run since 1912.
The BBC has reported that Iraola, who is leaving Bournemouth at the end of the season, is under consideration to take over at Stamford Bridge in the summer.
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Chelsea have opted to appoint Calum McFarlane as interim boss until the end of the campaign, with a permanent appointment to come before next season.
Iraola, along with Fulham’s Marco Silva and former Dortmund boss Edin Terzic are reportedly on the Blues’ list to take on the role.
But BBC senior football correspondent Sami Mokbel said his sources have told him that Iraola needs convincing to take on the role.
Iraola was asked about potential links to Chelsea after last night’s draw with Leeds and reiterated that his complete focus is on his job at the Cherries.
“I think I said it when I announced that I was not continuing here, for me now it's about Bournemouth, four games,” he said.
“We have an incredible position, incredible fight.
“Past week you were asking me about other clubs, I don't know why I remember exactly which ones, but also as a sign of respect for Bournemouth I cannot talk right now about my future because it's not what worries the Bournemouth supporters.”