Specialist ZF followed with its own eight-speed shifter, which has featured in a wide range of Audi, BMW, Chrysler and Jaguar models.
According to US industry paper Automotive News, suppliers have quietly tipped that development of the new transmissions is in the early stages - although neither carmaker has offered any confirmation.
A GM spokesperson reportedly told the paper that discussions between the two brands are ongoing, focusing on the joint development of "a variety of all-new fuel-efficient transmissions".
The report adds that GM is expected to build the nine-speed unit, destined for front-wheel-drive models, while Ford will produce the 10-speed for rear-wheel-drive and performance models.
For now, GM is understood to be developing its own eight-speed shifter, expected to debut in a new Cadillac model in the coming year.
Ford has also been working on its own eight-speed unit, although recent reports suggest that this project has been binned in favour of the new joint venture.
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