BBC Sport confirmed that the Citizens will pay an initial £32m for the 22-year-old, with a further £2.2m available in add-ons.
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Allan is expected to undergo his medical in the coming days before completing his move to the Premier League champions.
The Brazilian has been targeted as a replacement for compatriot Savinho, who is set to join Tottenham.
Meanwhile, City remain in talks with Spurs over the potential sale of Egypt forward Omar Marmoush.
There is optimism the deal could be completed before the September 1 transfer deadline, although some details are still being negotiated.
Nico Gonzalez could also leave City, with Newcastle interested in the Spanish midfielder.