We investigate active galactic nuclei (AGN) candidates within the FourStar Galaxy Evolution Survey (ZFOURGE) to determine the impact they have on star formation in their host galaxies. We first identify a population of radio, X-ray, and infrared-selected AGN by cross-matching the deep Ks-band imaging of ZFOURGE with overlapping multiwavelength data. From this, we construct a mass-complete (log(M*/M_{sun}_)>=9.75), AGN luminosity limited sample of 235 AGN hosts over z=0.2-3.2. We compare the rest-frame U-V versus V-J (UVJ) colours and specific star formation rates (sSFRs) of the AGN hosts to a mass-matched control sample of inactive (non-AGN) galaxies. UVJ diagnostics reveal AGN tend to be hosted in a lower fraction of quiescent galaxies and a higher fraction of dusty galaxies than the control sample. Using 160{mu}m Herschel PACS data, we find the mean specific star formation rate of AGN hosts to be elevated by 0.34-/-0.07dex with respect to the control sample across all redshifts. This offset is primarily driven by infrared-selected AGN, where the mean sSFR is found to be elevated by as much as a factor of ~5. The remaining population, comprised predominantly of X-ray AGN hosts, is found mostly consistent with inactive galaxies, exhibiting only a marginal elevation. We discuss scenarios that may explain these findings and postulate that AGN are less likely to be a dominant mechanism for moderating galaxy growth via quenching than has previously been suggested.