The three Baltic states are part of the Russian energy grid but plan synchronizing to the EU's network instead.
Based on interviews Reuters had conducted, the agency claims hackers have made incursions into Baltic networks over the past two years, similar to attacks in Ukraine that did considerable damage in that country.
Reuters' sources say Russian state organizations are suspected of being behind the campaigns. However Reuters was unable to independently verify the allegations.
At the end of 2015, hackers managed to disrupt operations of a Baltic energy grid with a distributed denial of service attack, without causing blackouts however, a source told Reuters. Investigations are still ongoing.
The source also told Reuters that suspected Russia-backed hackers had targeted a Baltic petrol-distribution system at around the same time as well with a similar attack.
Though the incidents date back to about a year and a half ago, cyber security consultants are still investigating some of them.
They say hackers can remain undetected for months inside systems, like in Ukraine where hackers had infiltrated the grids there for months before causing a blackout.
"It's the same kind of slander as all the other similar accusations," Kremlin spokesman Dmitry Peskov said when asked by Reuters about the possible hacks.
Russia has never cut power flows to the Baltic states or threatened to do so.
NATO and cyber security experts told Reuters they believe hackers are testing the Baltic energy networks for weaknesses, becoming familiar with how they are controlled in order to be able to shut them down at will.
A security official based in the Baltics told Reuters cyber attacks usually increased when Russia carried out large military exercises near its borders with the Baltic states.