Deila, who discovered his competitive debut will be against KR Reykjavik, confirmed talks were ongoing with former Hearts and Sunderland goalkeeper Craig Gordon but he warned Celtic fans not to expect imminent incoming transfer activity.
And he stressed that his main transfer focus was hanging on to the players who have taken Celtic into the Champions League in recent seasons, after the likes of goalkeeper Fraser Forster and centre-back Vigil van Dijk were linked with moves abroad.
Celtic face four pre-season friendlies in Austria before taking on KR in mid-July in the second qualifying round of the Champions League.
But when asked whether he expected new players to arrive before his first game, Deila said: "I don't think that will be possible.
"We have just been starting there. I'm used to people coming up with a lot of names but I haven't read the papers so I don't know the names.
"We are going to get the squad better in time. We have to be prepared and look around us and find the best players for Celtic. That will take some time."
Deila added: "I haven't seen so much on the budget yet but I think everyone at the club knows what kind of task is in front of us and what we need.
"The most important thing is to keep the players. We know this team has got into the Champions League before and done well in the league, so that's a good confidence from me and for everybody. It's a good start."
Celtic have been linked with the likes of Sheffield United midfielder Stefan Scougall - who played under Deila's assistant John Collins at Livingston - and 23-year-old United States midfielder Mikkel Diskerud, who rejected Deila's attempts to sign him for Stromsgodset two years ago in favour of Rosenborg.
Deila said: "That's just rumours. We don't comment on names now. We have to see what we need and take it from there."
But free agent Gordon has been in talks with Celtic after appearing to win a lengthy battle with a knee injury.
"There's a process going on," Deila said.
"Of course we know that Craig has been a fantastic goalkeeper. He has struggled a lot with injuries in the last two years. We will see if things can happen but there is still a process."