Celtic look set to sign former Liverpool boss Brendan Rodgers
Earlier, Celtic's biggest individual shareholder Dermot Desmond said the club had interviewed "in excess of six" candidates.
And the Irish businessman described the Northern Irishman as "a great manager".
"We're excited about the managers we've interviewed and we've discussed," Desmond said. "Hopefully in the next few days we will decide, and enter negotiations."
Asked whether Rodgers was one of those interviewed, Desmond replied: "I can't tell a lie.
"He's a great manager. He's proved it at Liverpool and I think he's a worthy candidate for Celtic - as all the other candidates are."
Ronny Deila's two-year tenure at Celtic ended with Sunday's 7-0 win over Motherwell.
Under the Norwegian, the club won consecutive Premiership titles, taking their current run of Scottish top-flight crowns to five, with the previous three won under Neil Lennon.
However, they have not reached the group stages of the Champions League since Lennon's time in charge.
Rodgers and Scottish former Celtic defender Malky Mackay, 44, have spoken to the club about the vacancy.
Both started their managerial careers at Watford - Mackay had a spell in charge of Cardiff City, while Rodgers was at Reading and Swansea City before joining Liverpool.
Mackay was sacked by Wigan Athletic six months before Rodgers was let go by Liverpool in October.
Four other former Celtic players - David Moyes, Roy Keane, Paul Lambert and Lennon - as well as former West Brom boss Steve Clarke have also all been strongly linked with the job.
Celtic had released a statement saying there was no preferred candidate and that they would take their time over the appointment.