Ipswich Town boss Kieran McKenna is among the candidates to replace Brendan Rodgers at Celtic, Sky Sports News understands.
Ex-Celtic manager Ange Postecoglou has also been linked with a return to the club. The 60-year-old is out of work after being sacked by Nottingham Forest after just 39 days.
Former Celtic boss Martin O'Neill and former player Shaun Maloney are in interim charge, with Celtic in action against Falkirk on Wednesday before an Old Firm League Cup semi-final against Rangers on Sunday.
McKenna, 39, has been linked to the Man Utd, Chelsea and Brighton jobs in recent seasons, having guided Ipswich to back-to-back EFL promotions and a first Premier League campaign at Portman Road for 22 years.
That season did end in relegation, with Ipswich now 12th in the Sky Bet Championship.
O'Neill says he is back at the club until a permanent manager is appointed, and believes Celtic will be searching for a "young manager with proven ability who has got a bit of a track record".
Chris Sutton says Postecoglou is the "obvious choice" to replace Rodgers at Parkhead.
"I think Ange Postecoglou would be a really smart appointment. He was loved the first time round," said Sutton.
"His brand of football went down well in Glasgow. He's out of work.
"I think that would be a pretty obvious choice, a good choice and bring a lot of positivity back to Celtic, which they need right now."
Martin O'Neill has revealed he had "10 minutes to decide" if he would return to Celtic following Brendan Rodgers' shock decision to resign.
The former manager has returned to the Parkhead club after 20 years to take interim charge of the side while the search for Rodgers' permanent successor takes place.
He is joined by former Hoops player Shaun Maloney, with Celtic in action against Falkirk on Wednesday before an Old Firm League Cup semi-final against Rangers on Sunday.
"Nervous excitement," the 73-year-old said when asked about his emotions. "I obviously want to do as well as I can. I'm looking forward to it - I think.
"This is a role where they're looking for a permanent manager. At this minute, I've been called in to do the job. Interim manager at this point - and that's the way it will remain.
"I didn't need to be told what's required. I got a call late afternoon, early evening from Dermot Desmond [Celtic's largest shareholder]. He said Brendan had resigned.
"People had been taken aback by that. I assumed nothing would happen until the end of the season for anybody. I was asked if I'd come in and hold proceedings until they found a permanent manager. I had 10 minutes to make up my mind, which I did."
Brendan Rodgers' broken relationship with the Celtic board was laid bare after his surprise resignation in an extraordinary statement from major shareholder Dermot Desmond.
Rodgers was accused of misleading fans over his contract talks and the club's transfer business as Desmond claimed the manager's "divisive" actions "fuelled hostility" toward the board and executive team.
Desmond put Celtic's recent struggles down to "one individual's desire for self-preservation" with the Scottish champions already eight points adrift of league leaders Hearts after failing to qualify for the Champions League.
Amid the backdrop of fan protests, which have called for the board to be sacked, Desmond blamed Rodgers for "contributing to a toxic atmosphere" at Celtic.
Sky Sports breaks down Desmond's stunning statement and why the relationship soured.
- Falkirk (H) - Scottish Premiership - Wednesday
- Rangers (N) - League Cup semi-final - Sunday
- Midtjylland (A) - Europa League - Nov 6
- Kilmarnock (H) - Scottish Premiership - Nov 9
- St Mirren (A) - Scottish Premiership - Nov 22 - live on Sky Sports
