Reaching ambitious voluntary medical male circumcision (VMMC) coverage targets requires a deeper understanding of the multifaceted processes shaping men's willingness to access VMMC. Guided by the Ideation Model for Health Communication, this population-based study identifies correlates of Zambian men's future VMMC intentions. Multistage cluster sampling was used to identify households with adult men in 14 districts. Multivariable Poisson regression with robust standard errors modelled associations of future VMMC intent with ideational factors (e.g. perceived benefits and barriers) and sexual behaviours respectively. Forty per cent (40%) of uncircumcised men ( = 1 204) expressed future VMMC intentions. In multivariable analysis, VMMC intent was associated with secondary education or higher (Adjusted Prevalence Ratio [APR] 1.30, 95% Confidence Interval [95% CI]: 1.02-1.66), perceiving VMMC to increase sexual satisfaction (APR 1.45, 95% CI: 1.11-1.89), reporting distance to services as a barrier to VMMC uptake (APR = 0.54, 95% CI: 1.27-1.87), unprotected last sex (APR 1.54, 95% CI: 1.11-2.14), and ≥ 2 sexual partners in the past 12 months (APR 1.45, 95% CI: 1.05-1.99). Being aged ≥ 45 years (vs 18-24 years: APR 0.23, 95% CI: 0.13-0.40) and perceiving that circumcision: (1) is unimportant (APR 0.71, 95% CI: 0.51-0.98); (2) is incompatible with local customs (APR 0.41, 95% CI: 0.18-0.94); or (3) reduces sexual satisfaction (APR 0.10, 95% CI: 0.02-0.62) were inversely associated with future VMMC intent. Demand-creation efforts must confront salient cognitive and social barriers to VMMC uptake, including concerns around incompatibility with local customs. Simultaneously, promotional efforts should emphasise relevant VMMC benefits beyond HIV prevention that resonate with men (e.g. penile hygiene) without reinforcing harmful gender norms.