The governing body wants all competitors to share common internals but have their own "team specific" gearbox casings on which the suspension is hung.
Apart from the tyre tender that was won last year by Pirelli, this is the first formal indication of a key element of the post-2020 rules package.
Potential suppliers have until March 15 to make their submissions, while the FIA says a decision will be announced between April 15 and 30.
A common cassette will represent a huge change to the way many F1 teams work.
Alfa Romeo and Haas currently use a complete Ferrari gearbox package, while Racing Point employs one from Mercedes and Toro Rosso shares the same unit as sister team Red Bull Racing.
A team specific casing will also make it harder for partner teams to share suspension components.
Gearbox specialist Xtrac has been mentioned in the paddock as a leading candidate for the tender, but there remains a possibility that an F1 team could win the bid and supply the whole field.
The tender, published on Monday reads, "The aim of single source supply is to retain current levels of F1 gear change performance for all cars at a much reduced cost to the competitors while also removing the requirement for teams to design or source their own gearboxes.
"The unit can be carried over between seasons so removing the need for costly continual performance development.
"In order to retain competitor's own freedoms for suspension and for the gearbox aero surfaces, the outer housing will remain team specific (designed and produced by the competitor) with the common, self-contained gearbox cassette mounted inside."
The FIA insists that the new gearboxes will be similar to current models, although there will be a move from the current eight gears to seven.
The tender also contains hints about the direction the rules are taking for 2021, including details of a more powerful MGU-K, which will provide 30kW more than it does at the moment.
"It is anticipated that significant effort should be applied to achieving a minimum size and weight for the unit, but it is also acknowledged that there are some factors that will make this difficult.
"Firstly, we need to achieve excellent reliability in the face of a life requirement of around 5000km. Secondly, there will be an average input speed increase of around 14% from today.
"Thirdly, there should be some power increase for 2021 relative to today, not just because of natural development, but also because of a 30kW increase in the MGUK output."
The FIA says that supply is based on a figure of four units per season, but the detailed numbers related to mileage and usage in the tender make provision for a calendar of up to 24 races.
"The unit will need to be designed in conjunction with all the existing competitors and PU suppliers to ensure it can function as well as possible in all cars and best endeavours should be made to satisfy as many competitors and PU supplier requests as practical in a unit for everyone.
"Clearly, the competitors that currently produce their own gearboxes will have knowledge built up that should be sought and taken account of if possible.
"In particular, their best design practices should be sought and a coherent set of design practice actioned during the process."
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