Former boss Neil Lennon is also in the running.
The Hoops won the league under Deila last season and look odds to claim it this season however they have failed in European competition and last week lost to Rangers in the SFA cup semi final.
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Deila says it's vital that the club comes first and now the team and the Club can be the focus as they enter this final important period of the season.
Lennon says he'd give serious thought to managing the club again.
