Start midfielder Ajer, 17, has returned to his native Norway following a one-week trial at Celtic.
"When it [the transfer window] is closed we will say something if he does [join]," said Deila of his countryman.
Asked about a potential loan deal for teenage Manchester City winger Patrick Roberts, Deila replied: "I can't comment on anything."
Roberts, 18, has played three times for City after signing from Fulham, where he made 22 appearances. He has also played up to England Under-19 level.
Celtic have already signed Danish defender Erik Sviatchenko from Midtjylland and Ryan Christie has been recalled from his loan spell at Inverness Caledonian Thistle.
"I'm happy with what we have got in," said Deila.
"It is a very difficult window. The teams around us don't want to lose players when they are in the middle of the season but we'll see.
"We work on and everybody in the club is looking for options and seeing what is possible."
Reigning champions Celtic, top of the Premiership and also through to the fifth round of the Scottish Cup, will seek to maintain their hopes of a domestic treble when they face Ross County in Sunday's League Cup semi-final.
The tournament was Deila's first trophy win as Celtic manager last season and preceded the club's fourth straight league success.
St Johnstone face Hibernian in the first semi-final on Saturday and Deila has urged his players to maintain their recent form, which has yielded five straight wins in all competitions and 19 goals along the way.
"We have taken some steps now, lately, and we are getting some rest and you can see that it puts a lot of energy into the boys," added Deila.
"If we keep the tempo and intensity that we had in the last games, we know that we can beat anybody.
"To step up is important, you have to develop yourself during the season and you need to get better and better.
"If you do that then you have a chance to fight for trophies.
"To play semi-finals is something that we enjoy. We did it twice last year and we had a final as well and we really, really want to play here in March [at Hampden for the League Cup final] as well.
"We're looking forward to it. This is a big, big opportunity for us."
Ronny Deila says "nothing is finished" regarding Celtic's interest in Kristoffer Ajer.