City have long held an interest in the 14-year-old and had their initial bid of the same value rejected back in January.
Ogwuru since became available for free as a result of Bolton’s financial problems and subsequent administration.
A number of clubs had made approaches to the youngster’s family as a result, but City have gone back to Bolton’s administrators with their original offer, which covered their obligations regarding training fees set out by the league’s Elite Player Performance Plan regulations.
City’s offer also includes a number of performance-related add-ons that will apply to Ogwuru’s time with the club’s various youth teams. Should he reach the first team in the future, Bolton could receive a seven-figure sum.
Ogwuru has been monitored by England scouts with a view to capping him at youth level in the coming years, and City plan to put him straight into their Under-15 team for the age group’s upcoming campaign.
He has caught the eye of scouts across the north west in recent months, with his size and poise in front of goal helping him stand out.
Ogwuru will be among a number of City youngsters hoping to follow in the footsteps of Phil Foden, who has been with the Blues since he was six years old and is now a member of Pep Guardiola's senior set-up.
Foden made his first appearance in a Guardiola squad in December 2016, and over the past two seasons has gained more and more first-team experience.
The England youngster is also expected to play even more of a role in the Premier League next season, having made three starts in 2018-19.
Other youngsters, including recent academy recruits, have also shown that opportunities exist within City's youth structure, such as 16-year-old Ben Knight, who signed from Ipswich last summer for £700,000 and was put straight into older age groups.
Knight, who had a rival offer from Tottenham, played an instrumental role in City's Under-18s getting to the FA Youth Cup final.