Boubaker al-Hakim is a member of the extremist Islamic State (IS) group who last month claimed responsibility for assassinating two secular politicians, Chokri Belaid and Mohamed Brahmi, in Tunisia in 2013.
He was previously part of the "Butte-Chaumont network" in Paris -- alongside Kouachi -- that helped send fighters to join Al Qaeda in Iraq in the mid-2000s.
Kouachi is wanted along with his brother Said for the deadly attack on satirical magazine Charlie Hebdo on Wednesday that left 12 people dead.
Hakim "represents the link between the Kouachi brothers and (IS)," said researcher Jean-Pierre Filiu, a leading expert on radical Islam at Paris's Sciences Po university.
"It is impossible that an operation on the scale of the one that led to the massacre at Charlie Hebdo was not sponsored by Daesh," he claimed, using an alternative name for IS.
No group has yet claimed responsibility for the Charlie Hebdo attack, "but it is certain that (IS) is closely following it and waiting to see how it ends," said Filiu.
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"I am sure that the video claiming responsibility is already prepared."
He added that Hakim is not a very senior figure in IS, but gained respect within the movement after killing Belaid and Brahmi.
Hakim claimed responsibility for the murders in a video released last month that was filmed in IS territory somewhere in Iraq or Syria.
Born in 1983, he is only around a few months younger than Kouachi and grew up in the same area of Paris -- the 19th arrondissement -- where the "Butte-Chaumont network" was established.
Both men were arrested and convicted together in Paris in 2008 for their role in the network.
Hakim was sentenced to seven years for running a way station in Damascus for young French Muslims en route to fight US forces in Iraq. Kouachi received three years.
"Hakim, and no doubt Kouachi, rejoined Al Qaeda's Iraqi networks after they were released from prison and accompanied them in their transformation into Daesh," said Filiu.
"The combat experience they acquired was useful in the cold-blooded assassinations they have carried out since."