The invariant mass spectra of phi-->K+K- are measured in 12 GeV p+A reactions in order to search for the in-medium modification of phi mesons. The observed K+K- spectra are well reproduced by the relativistic Breit-Wigner function with a combinatorial background shape in three betagamma regions between 1.0 and 3.5. The nuclear mass number dependence of the yields of the K+K- decay channel is compared to the simultaneously measured e+e- decay channel for carbon and copper targets. We parameterize the production yields as sigma(A)=sigma0Aalpha and obtain alphaphi-->K+K- -alphaphi-->e+e- to be 0.14+/-0.12. Limits are obtained for the partial decay widths of the phi mesons in nuclear matter.