Step 1: Every real source can be modelled two equivalent ways: a Thevenin model, a voltage source with a series resistance, or a Norton model, a current source with a parallel resistance.
Step 2: For a source to behave as an ideal voltage source, its Thevenin series resistance must shrink to zero, so none of the source voltage is dropped internally. By duality, for a source to behave as an ideal current source, its Norton parallel resistance must instead grow to infinity, so none of the source current leaks away internally.
Step 3: An infinite parallel resistance behaves like an open path, meaning all the current is forced out to the external circuit no matter what resistance that circuit presents. This duality confirms the internal resistance of an ideal current source is: \[ \boxed{\text{Infinite}} \]