SpaceX's next big booster is notionally known as BFR - Big F-ing Rocket [or Big Falcon Rocket]. (Like the B-52 is the BUFF - Big Ugly Fat F-er, it is a term of enderarment).
We know that it will use a cluster of Raptor engines, running on LOX/Methane. Raptor has been changing over time but appears likely to be in the 1 Million lb thrust or higher.
We know they want it to be reusable which in their current mode of operation requires a center engine to keep thrust levels manageable for landing, so likely a cluster of 3, 5, or 9 engines.
That puts some boundaries on likely sizes of the core.
What will the BFR look like? This question may have to evolve over time as more information is released.