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.
- Rodgers resigns as Celtic manager as O’Neill returns
- Scottish Premiership games coming up live on Sky Sports
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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”.
Sutton: Ange smart choice to replace Rodgers
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.”
‘Toxic’ – How Rodgers’ relationship with Celtic board soured
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.
Celtic’s upcoming fixtures
- 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
