Even so, the Northern Irishman stopped short of making firm commitments, pointing to the Iheanacho situation.
Celtic had hoped to keep the Nigerian forward after his one-year deal, but he instead signed earlier this week for Bursaspor, newly promoted to Turkey’s second tier.
O’Neill said they believed an agreement with Iheanacho was in place, only for it to fall through, adding it was something they thought had been settled.
Chief executive Michael Nicholson conceded it has been “difficult” to strengthen the squad given competition from big-spending clubs in England’s top two divisions.
While reports indicated Bursaspor offered the 29-year-old a higher salary, O’Neill stressed that every transfer has two sides and that applies here as well.
He said he had believed a deal was agreed at the time, but that proved not to be the case and the player has moved on.
O’Neill had also hoped to keep Saracchi following the 28-year-old left-back’s loan from Boca Juniors.
The Uruguayan wrote on Instagram on Friday that he and his agent did everything they could to make a return to Glasgow happen.
However, O’Neill said that although Saracchi performed very well for the club, circumstances meant a permanent move was never likely.
Celtic begin their Premiership campaign at home to Dundee on 3 August.