The man being investigated by Norwegian police over the attack on Kenya's Westgate shopping centre is Hassan Abdi Dhuhulow, BBC Newsnight has learned.
The 23-year-old Norwegian citizen of Somali origin is suspected of helping to plan and carry out the attack.
BBC Newsnight has spoken to a relative of his in Norway who said he left the town of Larvik for Somalia in 2009.
At least 67 people died in the attack in Nairobi, which the al-Qaeda linked group al-Shabab says it carried out.
Last week Norway's intelligence agency, the PST, said it had sent officers to Kenya to verify reports that a Norwegian citizen had been involved in the assault on the shopping centre, which began on Saturday 21 September and lasted four days.
It is unclear how many militants were involved. Police had initially estimated that there were 10-15 attackers inside the complex, but the CCTV footage which has so far been released by the Kenyan authorities shows just four men.
Hassan Abdi Dhuhulow is believed to be one of those four, the BBC's Newsnight programme has learned from sources in Kenya and Norway.
Forensic investigators are still combing through the rubble of Westgate - no bodies have yet been identified and it is not known whether the attackers are alive or dead.
Phone calls home
Dhuhulow was born in Somalia, but he and his family moved to Norway as refugees in 1999.
One relative, who spoke to our correspondent on condition of anonymity, said that Dhuhulow left for Somalia in 2009. He made infrequent, increasingly erratic, phone calls to the family, they said, the last one coming in the summer when he said that he was in trouble and wanted to return home.
On being shown the CCTV footage of the Kenya attackers by Newsnight, Dhuhulow's relative said: "I don't know what I feel or think... If it is him, he must have been brainwashed."
Reporting for Newsnight, Gabriel Gatehouse travelled to the coastal town of Larvik, 120 km (75 miles) south of Oslo, where Dhuhulow's family made their home.
Morten Henriksen, one of the family's former neighbours, has not seen Dhuhulow for years.
"He was pretty extreme, didn't like life in Norway… got into trouble, fights, his father was worried," Mr Henriksen said of Dhuhulow as a teenager.
When shown the CCTV footage of the four Kenya attackers he said that the one dressed in a black shirt or jacket could be Dhuhulow.
'Falling between cultures'
Stig Hansen, an expert on security and political Islam based in Norway, told Newsnight said that he was not surprised to learn that a Norwegian citizen was suspected of taking part in the attack.
He said that an estimated 20-30 Norwegians had gone to Somalia to sign up as fighters for the Islamist militant group al-Shabab.
"The biggest problem is the so-called 'Generation 1.5', those who weren't born in Norway, but came when they were quite young, falling between two cultures," he said.
"[Al-Shabab] need people who are quite ignorant about Somalia. That is in their interest because that will give them a more internationalist agenda. And it might also make them more dangerous when they return back to their home countries," he added.
There have been reports that a Kenyan al-Shabab leader whom US commandos targeted in a raid in Somalia on 5 October, but failed to capture, may have spent time in Norway.
Norway's TV2 reported that Abdukadir Mohamed Abdukadir, also known as Ikrima, had travelled to Norway and applied for asylum in 2004 but left in 2008 before there was a decision on his application.
Norwegian officials have not commented on the claims.
The full report aired on Newsnight on BBC Two at 22:30 BST on Thursday 17 October and is available on BBC iPlayer (UK only)