The Serie A club made an approach for the 22-year-old but it did not match Everton’s valuation.
Everton face a decision if Lazio up their offer for the former Aston Villa player, who cost them £10m in the summer of 2024.
Manager David Moyes has more options in midfield after Idrissa Gana Gueye returned from the African Cup of Nations and Harrison Armstrong impressed following his loan at Preston, while Kiernan Dewsbury-Hall has returned to fitness and James Garner committed his future to the Everton by signing a four-and-a-half year contract.
Iroegbunam has started 11 league games this season and made 35 appearances for Everton, who might want funds to strengthen their attack.
Moyes has been interested in Morocco striker Youssef En-Nesyri, though he now looks less likely to join Everton.
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