Itakura spent the 2021/22 season on loan at Schalke, as the Gelsenkirchen club managed to secure promotion to the Bundesliga.
The central defender, who can also deputise in defensive midfield, made 32 appearances in all competitions for Schalke last season, scoring four goals.
Schalke were priced out of a permanent move for the 25-year-old, amid reports that Borussia Monchengladbach had an agreement almost in place for the Japanese defender.
Now, with the Cityzens tipped to raise their asking price of £5m, which could also push Gladbach out of that race, the Hoops might still have a chance to sign Itakura.
The Scottish champions had been linked with the versatile defender from the time Ange Postecoglu took the reins last summer.
Having signed Cameron Carter-Vickers permanently from Tottenham Hotspur, Celtic are looking to further shore up their defence as next season will see Champions League football return to Parkhead.
Itakura has a year left on his contract with the Cityzens and is unlikely to break into their starting eleven given the options currently at Pep Guardiola’s disposal, making a permanent departure the likely option.