The Norwegian will leave the Scottish Premiership side at the end of the season.
The 40-year-old will leave the Hoops at the end of the season after a mixed two-year spell. While he appears set to secure his second consecutive Scottish Premiership title, and also won last year's League Cup, the Norwegian has received criticism for failing to take the team to the next level.
And ahead of his departure, Deila has suggested that his successor will have a better chance of doing well if they have an understanding regarding what the club is all about.
"If the next manager has a Celtic background that's not a negative thing," he told The Scottish Sun.
"It's not the most important thing, but it's a good thing.
"It's good to understand what Scottish football is all about and understand what the club is all about. I think that's an important thing."
While the former Stromsgodset boss is unlikely to have much say in who will take over from him, the Bhoys' hierarchy may be interested to know what he thinks about what is needed to enjoy success before they make their appointment.
And with several names being linked with the job, the likes of Roy Keane, David Moyes and Paul Lambert may all find themselves having a stronger chance of landing the position based on Deila's suggestion as they all enjoyed spells at the club during their respective playing careers.