The 29-year-old is currently a free agent following the expiry of his contract at the end of June and is training individually while considering his next move.
Iheanacho played a crucial role in Celtic's title-winning campaign last season, scoring several decisive goals to become a fan favourite at Parkhead.
"I'd like to do something with him (Iheanacho),” said O'Neill.
“That's the point. Of course, if we can do something relatively quickly, at least he then gets started in pre-season, which is really important for him.
"It's something he didn't have last year. After about three minutes, he was injured against Sturm Graz and he then hurt himself in the League Cup Final as well.
"So that would be nice. I'm definitely pursuing that at this minute."