We investigate the carrier-envelope phase (CEP) dependences of the single and double ionization processes of methanol (CH3OH) in an intense near-IR few-cycle laser field (2.1 × 1014 W/cm2) by the asymmetry in the ejection direction of CH3 + for the non-hydrogen migration channels and CH2 + for the hydrogen migration channels created through the C-O bond breaking after the ionization. Based on the absolute CEP values at the laser-molecule interaction point, calibrated by the method using intense few-cycle circularly polarized laser pulses [Fukahori et al., Phys. Rev. A 95, 053410-1-053410-14 (2017)], we confirm that methanol cations are produced by tunnel ionization and methanol dications are produced by the recollisional double ionization. We obtain the phase offset for the double ionization accompanying no hydrogen migration to be 1.85π as the absolute CEP at which the extent of the asymmetry becomes maximum. We interpret the phase shift of 0.85π from the phase offset of 1.0π for the tunnel ionization, estimated by a tunnel ionization model incorporating the chemical bond asymmetry, as the corresponding time delay associated with the electron recollisional ionization. The positive phase shift of 0.13π for the single ionization in the non-hydrogen migration channel is interpreted as the additional time (165 as) with which a methanol cation can be excited electronically prior to the decomposition. The additional phase shift of 0.22π for the single ionization in the hydrogen migration channel is interpreted as the additional time (280 as) required for a methanol cation to be excited electronically leading to the hydrogen migration prior to the decomposition.