The 19-year-old forward spent the majority of last season on loan at the Gigg Lane outfit, scoring 13 goals in 28 league games to help the Shakers seal automatic promotion to League 1.
Barker, who took charge of the club at the end of March following Alan Knill's switch to Scunthorpe United, had been hoping to secure Bury-born Ajose's services for a further year.
However, he told the Manchester Evening News that he expects the talented teenager to seal a big money move to a club in the second tier.
"We’re not going to go out and make wholesale changes. I know [the fans] are not happy about one or two players not coming in.
"But from what I can gather, Nicky Ajose is on the possible brink of a move to the Championship that involves a lot of money.
"Without being too negative, I think we have to accept the fact that we are trying to get this club to stand on its own two feet, so we wouldn’t put the club at risk by spending money we haven’t got."
Barker is optmisitic, though, that the successes of both Ajose and central defender Tom Lees, who spent last season on loan from Leeds United, will convice other higher-graded clubs to send them their young stars to gain regular first-team football.
"We’re a victim of our own success," he said. "But what I have tried to get across to other clubs is to say: ‘Give us your younger players and we will give them back and they will be worth money hopefully.’
"So, we will get that reputation, I hope, and we have based that around one or two other players we have shown interest in."
