The Sun says Mancini wanted assurances over his control of certain aspects at the club as he aims to push it forward to further success.
The Italian, 47, wanted more direct control over transfers and also requested a reorganisation of the medical department.
He has been at loggerheads with club chiefs about how that side of the operation at Carrington has been run for some time.
Mancini has also stood firm this summer over plans for the club's pre-season tour.
Club officials were hoping to have a longer tour of Asia to help boost City's global appeal.
But Mancini insisted on a short six-day trip and just two games.