Heighmap size recommendation for consoles

We are creating a game to deploy across multiple platforms, and would like it to be supported by the Xbox One, PS4, and PC. I develop 4096x4096 heightmaps to use for the world that are stitched together and are streamed in depending on player location. Is this heighmap size going to put a strain on the consoles?

It would be useful as a developer to have a reference to see the limitations of the consoles and suggestions on optimizing for multi-platform through better design.

Thanks for any help!