Speaking to reporters in Berlin, Oudkirk said the project could sanctioned under a bill passed in August 2017.
As Washington has declared that it might introduce sanctions against the Nord Stream 2 pipeline, authorities in Berlin have said that such a move won't guarantee the growth of imports of liquefied gas from the US.
As with Russia's existing Nord Stream pipeline, the route bypasses not only Ukraine, but also the Baltic states and Poland - and is seen as a "political project" rather than an economic one.
She has specified that this means that any pipeline construction project in the world could potentially be under sanctions.
"After our exit from the European Union, will this be a sensible extra measure that we might take that might assist with our diplomatic efforts?"
The US push came a day before Chancellor Angela Merkel travels to Sochi to meet Russian President Vladimir Putin for talks that will touch on Nord Stream 2, as well as the US decision to withdraw from the Iran nuclear deal.More news: Yanny or Laurel? Soundbite still has internet divided
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Despite taking a hard line against Russian Federation in recent years over its aggression in Ukraine and other matters, Merkel has defended the pipeline project, saying Germany badly needs to secure its gas supplies. At the same time, Oudkirk has not specified what kind of devices are in question.
Jens Mueller, a spokesman for Nord Stream 2, dismissed concerns from the USA and several European countries, saying the new pipeline would merely be one of many sources of natural gas for Europe.
According to her, the undersea pipeline will allegedly provide Russia with an opportunity to install surveillance equipment beneath the Baltic Sea and may also increase Europe's reliance on Russian natural gas supplies.
"Germany is not doing anything against the interests of Ukraine".
Merkel sent her economy minister, Peter Altmaier, on a frantic diplomatic trip to Moscow and Kiev this week in an effort to secure a deal that would keep some gas flowing through Ukraine, which now earns up to 2 billion euros a year from transit fees.
Mr Whittingdale said: "Does he share the widespread concern about the proposed Russian gas pipe line Nord Stream 2".