The 73-year-old last managed in 2019 during a brief spell at Nottingham Forest after his time as Republic of Ireland manager came to an end the year before.
His tenure at Celtic was iconic for the club’s supporters, with few held in higher regard than O’Neill.
He won three league titles, three Scottish Cups, a Scottish League Cup and steered Celtic to the Uefa Cup final.
“It’s short term. Celtic are probably stunned at the news Brendan left. they are obviously seeking a permanent manager, so it’s a short term fit,” insisted O’Neill, who has brought in Shaun Maloney to assist him.
“Interim does mean interim. It’s as simple as that. Celtic are looking for I assume a young coach with proven ability. We want to pull the club forward now.
“Naturally, I had a super time at Celtic, it was a privilege. I can’t emphasise enough, it’s short term until a permanent manager is appointed. I’ll just keep the seat warm.
“I might just call Henrick Larsson and ask him if he’s been staying in the gym.”
The Scottish Premiership champions are eight points behind early pacesetters Heart of Midlothian after losing 3-1 at Tynecastle on Sunday.
Celtic have also had an underwhelming European campaign and difficult transfer window.
In an astonishing letter to fans, Desmond challenged Rodgers’ assertion that he was not formally offered a contract extension, denied that signings were imposed upon the manager, and criticised his “desire for self-preservation at the expense of others”.
“In reality, he was given final say over all football matters and was consistently backed in the recruitment process, including record investment in players he personally identified and approved.
“Regrettably, his words and actions since then have been divisive, misleading, and self-serving. They have contributed to a toxic atmosphere around the club and fuelled hostility towards members of the executive team and the board.
“What has failed recently was not due to our structure or model, but to one individual’s desire for self-preservation at the expense of others.”
Rodgers has been approached for comment.