Corporate jet pilot reported a near miss while on approach with another aircraft performing a VFR practice instrument approach to a nearby airport. Pilot took evasive action and continued approach.

Narrative

Cleared for the ILS Z 08 BUR. ATC advised us that Aircraft Y was flying a practice VOR approach into VNY. I reported 'negative contact' on that traffic.The VOR approach parallels the Burbank 08 localizer quite closely.A couple of miles prior to crossing over the Van Nuys airport; the controller urgently started yelling at us to start an immediate climb due to traffic. The TCAS did not provide an RA; but the flight technician sitting on the jump seat pointed out the aircraft; which was at our altitude at our 10:30 to 11:00 position and had turned into our path. When I visually acquired the target it was wing up; estimating 60 degrees of bank. I instructed the PF to climb immediately.Based on aircraft size; our best estimate puts Aircraft Y 300 ft. away horizontally; at our altitude. We heard a 'Traffic' call from the TCAS; but no RA. After climbing above the traffic; the controller cleared us for the visual approach to runway 8 and we landed uneventfully.The VOR approach into Van Nuys has a procedure turn to the south at CANOG; so perhaps that explains the turn toward the Burbank localizer? Perhaps Aircraft Y pilot was starting the missed approach early. Perhaps they were simply off course; owing to the vagueries of flying a VOR needle when so close to the station. Either way; this seems like a poor setup by the controller. Since the VOR-A into Van Nuys and the ILS 08 localizer for Burbank are on closely space parallel courses; it would be prudent to consider them together and not put a slow Aircraft Y in front of a fast Aircraft X. There are already so many RAs when flying the Burbank ILS over the VNY traffic pattern.