  Close-in gas giants are expected to have a strong magnetic field of $\sim
10-100$G. Magnetic fields in extrasolar giant planets are detectable by future
radio observations in $\gtrsim 10$MHz and the spectropolarimetry of atomic
lines. In contrast, the elusive interiors of exoplanets remain largely unknown.
Here we consider the possibility of inferring the existence of the innermost
cores of extrasolar giant planets through the detection of planetary magnetic
fields. We simulated the long-term thermal evolution of close-in giant planets
with masses of $0.2-10M_\mathrm{Jup}$ to estimate their magnetic field
strengths. A young, massive gas giant tends to have a strong magnetic field.
The magnetic field strength of a hot Jupiter is insensitive to its core mass,
whereas the core strongly affects the emergence of a planetary dynamo in a hot
Saturn. No dynamo-driven magnetic field is generated in a hot Saturn with no
core or a small one until $\sim 10-100$Myr if metallization of hydrogen occurs
at $\gtrsim 1-1.5$Mbar. The magnetic field strength of an evolved gas giant
after $\sim 100\mathrm{Myr}$ is almost independent of the stellar incident
flux. Detecting the magnetic field of a young, hot Saturn as a good indicator
of its core may be challenging because of the weakness of radio signals and the
shielding effect of plasma in the Earth's ionosphere. Hot Jupiters with
$\gtrsim 0.4M_\mathrm{Jup}$ can be promising candidates for future ground-based
radio observations.
