Moscow issued an worldwide arrest warrant for Krasikov in 2014 only to silently withdraw it a year later.
Khangoshvili, a 40-year-old Georgian who fought against Russian Federation in Chechnya and had links with Georgian intelligence, was shot dead from behind by a cyclist in broad daylight in Berlin's Kleiner Tiergarten park in August.
The August 30 investigation did not establish the suspect's real identity. But in a statement on December 3, Bellingcat claimed that the suspect who had traveled to Berlin under the Sokolov alias is in reality 54-year-old Vadim Krasikov.
As with the murder of Khangoshvili, the 2013 victim was shot by a man who approached him on a bicycle.
Russian Federation put Krasikov on an Interpol wanted list but later withdrew his name and "facilitated the issuance of a new, false identity for him", Bellingcat said.
But the Russian government's unwillingness to illuminate the case raised suspicions.
"We have evidence that a foreign intelligence agency was behind it and therefore the case is going to be taken over by the federal prosecutor this week", said the source, who declined to be named. Other outlets carried similar claims.
"The Federal Prosecutor's Office suspects Russian state agencies of having commissioned the murder", the German weekly Der Spiegel reported, adding that federal prosecutors were preparing to step in "in the coming days".
Relations between Britain and Russian Federation plunged into a deep freeze after the incident.
German media have compared the attack on Khangoshvili to the attempted murder of Russian former intelligence agent Sergei Skripal and his daughter in the United Kingdom previous year.
Chechnya is now run by Ramzan Kadyrov, a former rebel who switched sides and is now fiercely loyal to Russian President Vladimir Putin.
Der Spiegel said police had recovered an air ticket from the suspect for Moscow for the day after the attack and a large sum of cash in his apartment.
Khangoshvili fled to Germany after surviving an assassination attempt in the Georgian capital Tbilisi in 2015.
The man has been charged with murder but has reportedly refused to speak to investigators.
The suspect's passport number had been traced back to a unit of the Russian interior ministry, which was known to have delivered identity documents for Russian military intelligence.
Russian Federation has not responded to the reports, although a spokesman did say in August that the killing had nothing to do with Russian Federation or its authorities.