The suns density is greatest in which region

The sun is most dense at its core.  It forms 10% of the sun's mass.   Because of the enormous amount of gravity compression from all of the layers above it, the core is very hot and dense.

The sun's core is about 16 million K and has a density around 160 times that of water. This is over 20 times denser than the dense metal iron which has a density of 7 times that of water.  However the sun's interior is still gaseous all the way to the very center  because of the extreme temperatures. There is no molten rock like that found in the interior of the earth.