However, the man who replaced Neil Lennon has yet to spend any of the transfer kitty he has available as the 23-year-old Norwegian striker has joined from Cardiff on loan until January.
Deila's first recruit, Craig Gordon, was a free agent when he accepted a two-year deal.
So the funds the Hoops boss has it his disposal remain intact.
In fact, they are about to be increased by the imminent sale of Tony Watt to Standard Liege.
Deila refuses to be pushed into any kind of panic buying, preferring to continue his in-depth analysis of the squad he already has. And Berget will also be put under the microscope to see if Deila believes it is worth exercising the option to buy which the club have negotiated with Cardiff.
Having arrived at the Bluebirds only in January, and having made just two appearances for them, the asking price for the man who has won four full caps will be minimal.
If he can recapture the form which saw Udinese take him to Italy as a teenager, that would be a very good piece of business.
Deila already knows what he has to offer as he had him on loan while manager of Stromsgodset in 2010.
And Berget was a key player in the Molde side which Stromsgodset beat to the Norwegian title last year.
He can play as a striker, but prefers to operate just behind or in a slightly wider position, which fits well with the 4-3-3 Deila likes to deploy.
Berget's disappointing experience at Cardiff has done nothing to dent his confidence, and he said: "I can play almost any role attacking-wise.
"I make things happen. I make goals happen and, hopefully, I can get the crowd going as well.
"It's going to be fun and exciting to play for the club."
Berget will be in the Hoops party which travels to Poland today for tomorrow's qualifier against Legia Warsaw.
They have until 24 hours before kick-off to register one extra player for the tie. And, if called upon, Berget is ready to do his bit.
He said: "We started back at Cardiff around the same time as Celtic, so I'm ready to play.
"Hopefully I can make an impression pretty soon.
"I'l be ready for the game if the manager wants me.
"I have some caps for the national team, which will help when it comes to playing in Europe.
"I've also played in the Europa League for Molde, so I've played in these sort of games before."