Methane (CH4) is a potent greenhouse gas and is the second-largest contributor to global warming after carbon dioxide (CO2). To meet ambitious climate change mitigation targets, it is crucial to effectively reduce the emissions of methane along with other greenhouse gases. The EU has introduced the Methane Regulation (Regulation (EU) 2024/1787), ultimately aimed at setting methane intensity thresholds for domestic production and imports of oil, coal and natural gas. However, the level of these thresholds is to be set in a later stage in a delegated act amending the regulation. Moreover, methane emissions from maritime transport will not be covered by the regulation. In this paper we examine the GHG reduction potential of imposing a methane emissions intensity threshold on imports of crude oil and natural gas. Due to high uncertainty on emissions associated with natural gas and crude oil production, we examine reduction potential based on average, minimum and maximum values. Moreover, we assess the effect of extending the scope to methane slip from LNG fuelled shipping. The results may inform the forthcoming discussion on the maximum threshold under the EU Methane Regulation. We find that in 2023-2024 methane emissions from oil and natural gas imports in the EU accounted for about 155 MtCO2e, assuming average production leakage rates. Crude oil imports contribute 105 MtCO2e, 27 MtCO2e came from LNG imports, and about 23 MtCO2e originated from pipeline transport. With the exception of natural gas and crude oil deliveries from Norway, none of the current imports comply with a methane intensity threshold of 0.2%, as proposed in numerous publications (see, e.g. European Parliament (EP) 2023). Holding patterns and volumes constant, setting a methane intensity threshold in the range of 0.2%-0.4% can reduce GHG emissions by 95-120 MtCO2e. Crude oil contributes about 66% to the total reduction. For crude oil, the largest total reduction with average production leakage rate comes from methane emissions from Libya, Kazakhstan and Nigeria contributing 13-16 MtCO2e, each, while for natural gas the USA and Algeria are the largest contributors with 12-13 MtCO2e, each. Taking crude oil and natural gas together, the USA and Algeria, each can contribute 12-13% to total emission reduction, if a 0.2% threshold is imposed. In particular for crude oil, the definition of the unit of the threshold is crucial: changing from mass-based to energy-based yields another 5-10 MtCO2e reduction, depending on the threshold level. Given that many of the leakage mitigation measures have negative abatement costs, the EU Methane Regulation could create a win-win situation.