However, the Northern Irishman did not want to give any firm promises, citing the example of Iheanacho.
Celtic wanted to retain the Nigerian striker at the end of his one-year contract, but instead he signed earlier this week for Bursaspor, who have only just been promoted to Turkey’s second tier.
“We thought we had a deal with Iheanacho and it didn’t go,” added O’Neill. “It was something we thought we had sorted out.”
Celtic chief executive Michael Nicholson has admitted it was proving “difficult” to add to their squad because they are competing with big-spending clubs in England’s top two divisions.
Reports suggested Bursaspor were able to offer the 29-year-old Iheanacho a higher salary, but O’Neill said: “There are two sides to every particular transfer as there is to every story.
“I thought we had a deal with him at the time. but seemingly that wasn’t the case and so he’s gone to pastures new.”
O’Neill had also hoped to retain Saracchi after the 28-year-old left-back’s loan spell from Boca Juniors.
The Uruguayan posted on Instagram on Friday that he and his agent “did absolutely everything within our power to make a return to Glasgow happen”.
However, O’Neill added: “Saracchi’s done very well at the football club and there’s circumstances which seemingly it was never going to happen.”
Celtic start their season at home to Dundee in the Premiership on 3 August.
