Context. Numerical studies as well as scaled laboratory experiments suggest that bipolar outflows arising from young stellar objects (YSOs) could be collimated into narrow and stable jets as a result of their interaction with a poloidal magnetic field. However, this magnetic collimation mechanism was demonstrated only for the simplified topology of the uniform poloidal magnetic field. Aims. We have extended the experimental studies to the case of a plasma outflow expanding in a region of strong poloidal magnetic field and then propagating through divergent magnetic field lines. In this case the magnetic field distribution is closer to the hourglass magnetic field distribution expected near YSOs. Our aim was to find out whether (and under what conditions) magnetic collimation is possible in such a strongly nonuniform B-field configuration. Methods. The experiments were carried out on the PEARL high-power laser facility. The laser produced plasma outflow was embedded in a strong (~10T) magnetic field generated by our unique magnetic system. The morphology and dynamics of the plasma were diagnosed with a Mach-Zehnder interferometer. Results. Laboratory experiments and 3D numerical modeling allow us to reveal the various stages of plasma jet formation in a divergent poloidal magnetic field. The results show (i) that there is a fundamental possibility for magnetic collimation of a plasma outflow in a divergent magnetic field; (ii) that there is good scalability of astrophysical and laboratory flows; (iii) that the conditions for the formation of a magnetic nozzle, hence collimation by poloidal magnetic field, have been met; and (iv) that the propagation of the jet proceeds unimpeded through the region of weak and strongly divergent magnetic fields, maintaining a high aspect ratio. Conclusions. Since we have verified that the laboratory plasma scales favorably to YSO jets and outflows, our laboratory modeling hints at the possibility of the YSO jet collimation in a divergent poloidal magnetic field.