Dalman revealed the newly promoted Premier League side made an offer he had no option but to accept given the details within the striker's contract.
Leicester manager Nigel Pearson is looking to build his squad ahead of their return to the top flight and has already signed Marc Albrighton, Matthew Upson and Ben Hamer.
Campbell was Cardiff's top scorer last term as they were relegated from the Premier League, and Dalman is keen for the forward to stay in south Wales and help fire the club back into the top tier.
"Leicester City have made an offer which triggers a release clause in Fraizer's contract," Dalman told Wales Online. "We don't want to sell him and would love him to stay but we had no choice because of the clause.
"We have to allow Fraizer to make his own decision but hopefully he can stay."
Campbell joined Cardiff from Sunderland in January 2013 and has scored 16 goals in all competitions for the club.