A Foreign Ministry spokesman declined immediate comment on the report but invited reporters to what he called an "informal briefing" on the issue.
BNS said the sources told it that the diplomat working in Vilnius had been ordered to leave Lithuania on suspicion of espionage and "seeking to influence Lithuania's determination to support Georgia amid its conflict with Moscow".
A diplomatic crisis between Georgia and Russia erupted after Georgian law enforcement officers detained several Russian officers on suspicion of spying for Moscow.
The suspected spies were later handed over to the Organisation for Security and Cooperation in Europe.
In 2004, Lithuania ordered out the Russian military attache and two other diplomats for alleged intelligence activities. Moscow retaliated by expelling the Lithuanian military attache.
The small Baltic state of Lithuania was a Soviet republic before gaining independence from Moscow in 1991.