The 38-year-old was appointed by the Scottish champions last Friday as a replacement for Neil Lennon, who decided to leave the club after four years in charge.
Deila arrives at Celtic Park with the club preparing for the defence of the title for a third successive season, and with expectations of Champions League football high following Lennon’s successful period in charge.
And Thompson, who played for Celtic between 2000 and 2007, reckons the Norwegian will take a short time to settle in Glasgow.
Speaking to Sky Sports News, Thompson said: “It will be difficult for him. He might need a period to settle in just to find out what it’s about, because it is a huge club with big demands.
“You can’t lose two games in a row. One game is bad enough, but if you lose two the pressure comes right on top.
“You find that out quickly and you have to deal with it
“Whoever was going to go in as manager on the back of the job that Neil had done, they’re expected to win the league but there is a demand there to do well in Europe.
“The fans will demand that they get in to the Champions League group stages and move on from there."