We explore X-ray emission from a sample of 18 He II lambda 1640 emitting star-forming galaxies at z similar to 2.3-3.6 from the VANDELS survey in the Chandra Deep Field South, to set constraints on the role of X-ray sources in powering the He II emission. We find that 4 He II emitters have tentative detections with S/N similar to 2 and have X-ray luminosities, L-X = 1.5-4.9 x 10(41) erg s(-1). The stacked luminosity of all 18 He II emitters is 2.6 x 10(41) erg s(-1), and that of a subset of 13 narrow He II emitters (FHWM(He II) <1000 km s(-1)) is 3.1 x 10(41) erg s(-1). We also measure stacked LX for non-He II emitters through bootstrapping of matched samples, and find L-X = 2.5 x 10(41) erg s(-1), which is not significantly different from LX measured for He II emitters. The LX per star formation rate for He II emitters (log (L-X/SFR) similar to 40.0) and nonemitters (log (L-X/SFR) similar to 39.9) are also comparable and in line with the redshift evolution and metallicity dependence predicted by models. Due to the non-significant difference between the X-ray emission from galaxies with and without He II, we conclude that X-ray binaries or weak or obscured active galactic nuclei are unlikely to be the dominant producers of He II ionizing photons in VANDELS star-forming galaxies at z similar to 3. Given the comparable physical properties of both He II emitters and non-emitters reported previously, alternative He II ionizing mechanisms such as localized low-metallicity stellar populations, Pop-III stars, etc. may need to be explored.