Context. Currently, the number of known planets around intermediate-mass stars (1.5 M⊙ < M⋆ < 3.5 M⊙) is rather low. As a consequence, models of planet formation derive their strongest observational evidence from the chemical signature of mostly low-mass (FGK) main-sequence (MS) stars with planets. Aims. We aim to test whether the well-known correlation between the metallicity of the star and the presence of gas-giant planets found for MS low-mass stars still holds for intermediate-mass stars. In particular, we aim to understand whether or not the planet-metallicity relation changes as stars evolve from the pre-MS to the red giant branch. Methods. We compiled the basic stellar parameters (metallicity, mass, and age) of a sample of intermediate-mass stars at different evolutionary phases with and without evidence suggesting that they host gas-giant planets. The metallicities of the different susbsamples were compared and set in the context of current models of planet formation and stellar evolution. Results. Our results confirm that pre-MS stars with transitional discs with gaps show lower metallicities than pre-MS ones with flat discs. We show a tendency of intermediate-mass stars in the MS to follow the gas-giant planet-metallicity correlation, although the differences in metal content between planet and non-planet hosts are rather modest and the strength of the correlation is significantly lower than for the less massive FGK MS stars. For stars in the red giant branch, we find a strong planet-metallicity correlation, compatible with that found for FGK MS stars. We discuss how the evolution of the mass in the convective zone of the star's interior might affect the measured metallicity of the star. In particular, if the planet-metallicity correlation were of a primordial origin, one would expect it to be stronger for less massive stars, as they are longer convective during the stellar evolution. However, within our sample, we find the opposite. Conclusions. The lack of a well-established planet-metallicity correlation in pre-MS and MS intermediate-mass stars can be explained by a scenario in which planet formation leads to an accretion of metal-poor material on the surface of the star. As intermediate-mass stars are mainly radiative, the metallicity of the star does not reflect its bulk composition but the composition of the accreted material. When the star leaves the MS and develops a sizeable convective envelope, a strong-planet metallicity correlation is recovered. Thus, our results are in line with core-accretion models of planet formation and the idea that the planet-metallicity correlation reflects a bulk property of the star.