In the ferromagnetic type-I clathrate Eu8Ga16Ge30, the divalent Eu ions are known to rattle among off-center positions in the tetrakaidecahedral cage. We have studied effects of Si substitution on the ferromagnetic state and the rattling motion of the Eu ions in Eu8Ga16Ge30 by measuring the magnetization M, electrical resistivity ρ, thermopower, specific heat C, and Eu partial phonon density of states (Eu pDOS) of Eu8Ga16−xGe30+x−y−zSiy□z (□ = vacancy, 0 ≤y≤ 7.3). Upon increasing y from 0 to 7.3, the lattice parameter decreases by 0.7%, which has no effect on the divalent state of Eu. The Curie temperature TC decreases from 36.2 K to 32.6 K, whereas the specific heat jump at TC, ΔC, increases twofold. For y= 0, both ρ (T) and dM(T)/dT exhibit anomalies below TC at T∗∼ 24 K, which are suppressed by applying magnetic field of 1 T. The anomalies at T∗ disappear by Si substitution at a low level, y = 3.7. The measured Eu pDOS indicates that the low-lying phonon energy of the Eu ions decreases with Si substitution. This softening means that the off-center rattling is changed to on-center one with large amplitude in an anharmonic potential. Based on these findings, we discuss relationship between the off-center Eu rattling and their collective magnetic behavior.