The Mirror says City are set to give Van Bronckhorst the chance to put himself in the frame to replace Guardiola by appointing him coach of their sister club in New York.
The Dutchman was handed an access-all-areas role at the club to learn about the inner workings of the City Football Group, which also includes New York and clubs in Spain, Australia, Uruguay and Japan.
The plan is for him to take over their MLS franchise after Domenec Torrent stepped down as head coach after New York's semi-final play-off defeat to Toronto.
Van Bronckhorst has visited both New York and Melbourne in the last two months and has also been observing Guardiola's coaching methods in Manchester.
Guardiola's contract expires in the summer of 2022 and City want a replacement in place who shares the same philosophy as the Catalan.