The White House in Washington, D.C.

Impeachment investigations may not do any favors for sitting presidents, but at least the e-discovery process won't suffer much.

Last week, CNN reported that the Justice Department had instructed the White House to preserve all documents related to the President's "meetings and phone calls with foreign leaders." And while many of those leaders may hail from countries with their own particular set of privacy regulations or national security laws, those shouldn't present too large an obstacle to the preservation mandate set before the White House.

Brian Hengesbaugh, chair of the global data privacy and security unit at Baker McKenzie, doesn't foresee a foreign entity fashioning a really strong privacy claim related to a call made with the American president.

"It's not that they could not," Hengesbaugh said. "I'm sure China could come up with a state secret argument about something that's being said, but whether they would actually be able to press it or not, it's probably unlikely."

Cross-border e-discovery, for instance, can occasionally be hampered by international privacy laws like the EU's General Data Protection Regulation (GDPR), which is heavily concerned with the way that personal data is handled while passing international borders.

While Hengesbaugh said many privacy laws around the world do have exemptions for national security considerations, those considerations are typically limited to their own country's governments.  In other words, don't expect foreign privacy regimes to bend over backwards to do the U.S. any favors.

"U.S. national security or a U.S. legal requirement wouldn't fit within the scope of that exemption because it's not recognized as being the same," Hengesbaugh said.

However, records related to Trump's phone calls with foreign leaders may not be generating much of a privacy risk anyway.

In the case of a call between two heads of state, data isn't technically crossing anywhere. And unless a foreign leader starts discussing his or her family, the content of a "business" call is unlikely qualify as personal data, "in which case information can be simply redacted and produced," said Eric Mandel, a consultant with e-discovery services provider Driven.

Still, Hengesbaugh said some foreign electronic communications laws require that consent to be obtained before a call is recorded. However, he thinks it's possible there could an implied consent when two heads of state initiate a phone conversation.

"I would think that there would be an understanding or an implied consent that not only is there probably a recording but there's probably 12 people listening at the same time, and then there's probably 15 others that are from other nations that are hacking the call as well," Hengesbaugh said.

Any notes or records that those 12 other people may generate from their participation from the call are also unlikely to fall subject to privacy claims given that the were probably created in Washington D.C. or somewhere in the U.S.

If a foreign government did want to have something redacted from a record or transcript, Mandel indicated that a dignitary could be sent before a judge. In that instance, courts are likely to balance the needs of the impeachment investigation against those of the foreign entity in question.

Still, countries hoping to get the entirety of a document sealed or redacted may be out of luck. "If you give [the court] all or none, the court is going to give you none," Mandel said.