Due to high efficiency, X-ray lasers based on transitions of Ni-like krypton (Kr<sup>8+</sup>) are being actively studied. The main focus is on an X-ray laser based on the conventional 3d<sub>5/2</sub>4d<sub>5/2</sub> [J=0] – 3d<sub>3/2</sub>4p<sub>1/2</sub> [J=1] transition at λ=32.8 nm. Gaseous krypton targets or krypton cluster jets are used in various experiments. X-ray lasers at 32.8 nm in a plasma formed by optical field ionization in a krypton cluster jet are widely used for research of nanoobjects. In this article, the possibility of creating an efficient X-ray laser in Ni-like krypton based on a transition with optical self-pumping 3d<sub>3/2</sub>4f<sub>5/2</sub> [J=1] – 3d<sub>3/2</sub>4d<sub>5/2</sub> [J=1] at λ=44.4 nm is predicted for the first time. The plasma filament is excited upon interaction of a jet of krypton clusters with an intense pump laser pulse. Optimal conditions to achieve the duration t<sub>las</sub> ≤300 fs of the X-ray laser radiation are determined. The optimal electron density is in a rather narrow interval in the range n<sub>e</sub> ~ 10<sup>21</sup> - 2×10<sup>21</sup> cm<sup>-3</sup>. The optimal electron temperature is several keV. It is likely that this explains the fact that no X-ray laser has been observed on this transition in Kr<sup>8+</sup> so far. The conversion factor per pulse is found to be ~5×10<sup>-5</sup>. For an X-ray laser operating on the conventional transition 3d<sub>5/2</sub>4d<sub>5/2</sub> [J=0] – 3d<sub>3/2</sub>4p<sub>1/2</sub> [J=1] at λ=32.8 nm, t<sub>las</sub> ≤ 300 fs can also be achieved; however, the conversion factor for this transition is times ~5 smaller than that for the former transition.