A P Cygni profile with absorption at 1.05 mu m was observed in three pre-maximum J-band spectra of the Type Ia supernova (SN) 1994D. The feature was not present in two post-maximum spectra. The line was attributed to Her 10830 Angstrom or Mg II 10926 Angstrom, based on a local thermodynamic equilibrium (LTE) treatment. The detection of He in the ejecta of a SN Ia would be useful for determining the pre-SN evolution and the explosion mechanism of SNe Ia, In this paper, synthetic spectra are presented for both the He and Mg models. The population of the He levels has been computed in non-local thermodynamic equilibrium (NLTE), including non-thermal excitation and ionization effects resulting from the deposition of gamma-rays from the decay of Ni-56 and Co-56. The J-band feature in the pre-maximum spectra can be reproduced either assuming the presence of a narrow shell, between 10000 and 12500 km s(-1), containing about 0.01 M. of He, or increasing the abundance of Mg by about a factor of 5 with respect to the W7 value, implying a Mg mass of about 0.08 M. above 10000 km s(-1). Both models are in good agreement with the optical spectrum. In particular, a strong He I 10830-Angstrom line does not imply a strong 5876-Angstrom line, because the departure coefficients of the 2p and 2s levels of Her differ by about an order of magnitude. Unfortunately, neither model is able to reproduce the sudden disappearance of the J-band feature in the post-maximum spectra. Possible explanations are discussed.