From the Boeing QRH:
There are some situations where the flight crew must land at the nearest suitable
airport. These situations include, but are not limited to, conditions where:
• the non–normal checklist includes the item “Plan to land at the nearest
suitable airport.”
• fire or smoke continues
• only one AC power source remains (engine or APU generator)
• only one hydraulic system remains (the standby system is considered a
hydraulic system)
• any other situation determined by the flight crew to have a significant
adverse effect on safety if the flight is continued.
Requesting priority handling without declaring an emergency is not contemplated in the ICAO rules and in general airline OPS regulations and does not ensure you will be assigned priority.
So, to comply with the Boeing rules, to my understanding, a PAN call would be applicable, upgradable to MAYDAY if conditions warrant.