Aina spent last season on loan at Torino from Chelsea, playing 29 times and scoring once for the Granata last season.
“We’ve redeemed Aina for €10m, as well as Cristian Ansaldi, and Koffi Djidji. Now Torino own all their players,” Cairo said at the Lega Serie A assembly held in Milan on Monday,” Torino president Urbano Cairo said.
“We fought for a European place until the end of the season. We were in the running for a Champions League place but missed out by a few points.
“We want to be ambitious. That’s why I intend to keep all my best players and strengthen the squad.
“I don’t want to talk about the possibility of Milan not participating in Europe next season. We’ll wait and see what the decision is first, then we can plan ahead.”
Torino finished in seventh place with 63 points last season, three shy of picking a Europa League spot.
Aina made Nigeria’s final squad for the 2019 Africa Cup of Nation billed to hold in Egypt between June and July.