Central defender Ajer joined the Scottish champions as a teenager from Start four years ago and has gone on to become a fixture in the Norwegian national team.
The 21-year-old will line up against former Norway star Solbakken’s Copenhagen side in the first leg of their Europa League last 32 tie in Denmark on Thursday.
Solbakken insists the financial gap between Copenhagen and Celtic means he cannot afford to shop in the same market as the Scottish champions but feels he should have been quicker off the mark when Ajer was breaking through.
“I don’t think we could afford any of Celtic’s players,” said Solbakken. “But maybe I should have signed Ajer when he was 17 and playing in Norway. We were probably too slow then.
“We knew about him very early when he was a striker and then a central midfielder at Start, their captain when he was very young. Maybe we should have pulled the trigger then. But that’s the only one I think we could have afforded in competition with Celtic.”
Copenhagen’s preparations for the tie have been far from ideal. They lost 1-0 to relegation strugglers Esbjerg in their first game after the Danish Superliga’s two-month winter break, then sold top scorer Pieros Sotiriou to Astana for £4 million this week.
Solbakken has also been left frustrated by an issue with training facilities after they returned from a warm weather camp in Portugal.
“We have suffered a little bit because there is no place to train due to weather,” he said. “We trained on a fourth division muddy pitch this week which is not for old knees.
“All those who were watching training on Tuesday must have thought it was a joke we were there, but that’s life for us at the moment.
“In the short term, losing Sotiriou might be a problem but we chose to do it because we have a financial responsibility.
“We are used to the winter break and we actually needed it this season. Unfortunately, we got a few injuries in Portugal and then the problem with the training pitch when we got back.
“But we are used to coming into this period of the season and catching up with teams who are more into their competitive matches. I don’t think Celtic will have an easy game on Thursday night but, yes, we have had our challenges.”