Amide proton transfer (APT) imaging is a variation of chemical exchange saturation transfer MRI that has shown promise in diagnosing tumors, ischemic stroke, multiple sclerosis, traumatic brain injury, etc. Specific quantification of the APT effect is crucial for the interpretation of APT contrast in pathologies. Conventionally, magnetization transfer ratio with asymmetric analysis (MTR ) has been used to quantify the APT effect. However, some studies indicate that MTR is contaminated by water longitudinal relaxation time (T ), and thus it is necessary to normalize T in MTR to obtain specific quantification of the APT effect. So far, whether to use MTR or the T -normalized MTR is still under debate in the field. In this paper, the influence of T on the quantification of APT was evaluated through theoretical analysis, numerical simulations, and phantom studies for different experimental conditions. Results indicate that there are two types of T effect (T recovery and T -related saturation), which have inverse influences on the steady-state MTR . In situations with no or weak direct water saturation (DS) effect, there is only the T recovery effect, and MTR linearly depends on T . In contrast, in situations with significant DS effects, the dependence of MTR on T is complex, and is dictated by the competition of these two T effects. Therefore, by choosing appropriate irradiation powers, MTR could be roughly insensitive to T . Moreover, in non-steady-state acquisitions with very short irradiation time, MTR is also roughly insensitive to T . Therefore, for steady-state APT imaging at high fields or with very low irradiation powers, where there are no significant DS effects, it is necessary to normalize T to improve the specificity of MTR . However, in clinical MRI systems (usually low fields or non-steady-state acquisitions), T normalization may not be necessary when appropriate sequence parameters are chosen.