Deila was in charge of Celtic for two years before he left his managerial role at the Scottish Premiership giants at the end of last season.
Former Liverpool manager Brendan Rodgers replaced the Norwegian at Celtic Park.
Ajer has been working with Rodgers in pre-season and will be aiming to establish himself in the Celtic first team this campaign.
The 18-year-old midfielder, who signed a pre-contract agreement with the Bhoys back in February, has revealed that he has been in touch with Deila.
“Ronny has text me to wish me good luck,” Ajer told The Glasgow Evening Times. “He text me after I had played centre-half here and told me to enjoy every moment of playing at Celtic Park.
“I also wanted to wish him good luck too because he brought me to the club and it was just the way that things happened that we did not work on the field together.”
Celtic are aiming to progress to the group stage of the 2016-17 Champions League campaign. The Bhoys will be favourites to clinch the Scottish Premiership title this season.
The Hoops have been quite busy in the summer transfer window, signing Moussa Dembele, Kolo Toure, Paul Joseph Crossan and Ajer so far.
The Hoops will take on FC Astana in the second leg of the Champions League qualifying third-round tie at Celtic Park in Glasgow on Wednesday evening.