Nancy's Haitian midfielder, Jeff Louis, is one of the names at the top of his shopping list, and an offer to his French club is imminent.
But the Hoops boss - while relieved to have seen his side reinstated to the competition after Legia Warsaw forfeited the victory in the second leg of their qualifier by playing an ineligible player - is demanding that a sense of perspective is retained by fans looking for new faces.
Yes, he has money to spend, even more if Fraser Forster and Virgil van Dijk move to England.
But, even with the carrot of Champions League participation possibly back in their hand, Deila admits they simply can't offer the wages which clubs in the two divisions down south can dangle in front of potential signings.
So, the side which lines up against the Slovenian champions away in Maribor a week on Wednesday will not show major changes from the one which lost 4-1 and then 2-0 to Legia before the second result was converted to a 3-0 win, allowing Celtic to go through to the play-offs on the away goal rule.
The Norwegian was critical of his squad after the Murrayfield defeat, but now insists he did not mean to suggest he had to perform wholesale surgery.
He is confident the squad he has can be improved, and, with a few more additions of quality, deliver the football - and results - he demands.
Deila said: "We need some new players, and our main task right now is to get them before the play-off round.
"With the chance to get to the Champions League, it could be easier to get them."
Deila appreciates Celtic have a wage ceiling, and supports their insistence on ensuring it remains intact.
So, while they can afford to compete with transfer fees, the disparity between what they can offer in wages compared to what is available in England is a major obstacle.
Deila has been in this position before, and explained: "It was the same with my old club, Stromsgodset. We could get the players in, but it was the salaries.
"You can't do it. You will ruin the whole club.
"And that's one of the things the fans should be proud of, and that I am proud of, that I've come to a club that has good organisation.
"That's important, and is going to be more and more important in the future.
"I can understand they want names. I understand that. When you are talking about Celtic, it is an unbelievably big club.
"And, if they had been in the Premiership, we would be fighting with Manchester City for players. But, we're playing in the Scottish league, and that is the difference."
Which is why he will be spreading his net wide and not trying to hook any big fish from ponds near to hand. Deila said: "If it was up to us, we would have a lot of players coming to Celtic.
"But the money is so much less in Scotland than it is in England.
"A Championshipo player is earning much more than they do in the Scottish league, and in Celtic.
"That wasn't the case around 2000 and 2005. The wages were near each other. Now, the gap is so big. And players want money."