Celtic were paid £9m in compensation by Leicester City last month for manager Brendan Rodgers and three members his backroom staff, according to a report.
The Foxes announced the Northern Irishman's appointment on February 26, bringing an end to his two-and-a-half year stay at Paradise.
Leicester had to hand over a large cash sum to land their top target, though, dwarfing the £4m package Everton recently agreed with Watford for Marco Silva.
The Telegraph reports that Celtic inserted the figure into the four-year deal Rodgers signed in April 2017, but that would have been reduced in a few months' time.
City were unwilling to wait until the summer, however, and the report suggests that they were happy to pay Celtic the £9m as it also allowed them to sign up assistant manager Chris Davies, first-team coach Kolo Toure and head of performance Glen Driscoll.
Rodgers has lost one and won one of his first two games in charge.