One of the possible sources of hadronic cosmic rays (CRs) are newborn pulsars. If this is indeed the case, they should feature diffusive gamma-ray halos produced by interactions of CRs with interstellar gas. In this paper we try to identify extended gamma-ray emission around young pulsars, making use of the 7-year Fermi-LAT data. For this purpose we select and analyze a set of eight pulsars that are most likely to possess detectable gamma-ray halos. We find extended emission that might be interpreted as a gamma-ray halo only in the case of PSR J0007 + 7303. Its luminosity accords with the total energy of injected cosmic rays similar to 10(50) erg, although other interpretations of this source are possible. Irrespectively of the nature of this source, we put bounds on the luminosity of gamma-ray halos which suggest that pulsars' contribution to the overall energy budget of galactic CRs is subdominant in the GeV-TeV range.