The Scottish champions are still on the lookout for a permanent manager following the disastrous and short tenure of Wilfried Nancy.
O’Neil took over on an interim basis following Nancy’s sacking, taking Celtic to the Premiership title with a 3-1 win over Hearts on the final day.
According to Sky Sports, Celtic have held talks with former striker Keane regarding the position now that he’s left Ferencvaros.
The club are also planning talks with O’Neil over the next 24 hours, however, to discuss whether the 74-year-old would like to properly come out of retirement and take the job.
If O’Neil doesn’t want to take the job, Celtic are still keen on offering him a possible position in the football operations side, or an advisory and consultancy role.