In this paper we consider codes in Fs×rqwith packing radiusRregarding the NRT-metric (i.e. when the underlying poset is a disjoint union ofschains with the same lengthr) and we establish necessary condition on the parameterss,randRfor the existence of perfect codes. More explicitly, forr,s≥ 2 andR≥ 1 we prove that if there is a non-trivial perfect code then (r+ 1)(R+ 1) ≤rs. We also establish a correspondence between perfect codes withr>Rand those withr=R. Using this correspondence we prove the non-existence of non-trivial perfect codes in the casess≥R+ 2 ands= 3 over non-binary alphabet.