"We're still awaiting clarification from the UK government about this issue and the implications of the new sanctions regulations for fields, but pending that clarification, we are making preparations to shut the field," a BP spokesman told AFP.
The shutdown of the Rhum field would take "several days", he added.
The Rhum field, lying 250 miles (400 kilometres) off Scotland's northeast coast in the North Sea, is a 50-50 venture between BP and the National Iranian Oil Company (NIOC) under a deal that pre-dates the 1979 Islamic revolution.
European Union foreign ministers last month approved tough sanctions targeting Iran's vital energy sector in order to bring Tehran back to the negotiating table over its uranium enrichment activities.
Rhum accounts for only a small part of BP's oil and gas production in the North Sea.
