Dhuhulow, 23, was born in Somalia, only moving to the town of Larvik as a refugee in 1999, when he was ten years old.
Relatives told the BBC that he had left Somalia in 2009, since when the only contact they had had had been through occasional phone calls.
"I don't know what I feel or think," one of Dhululow's relatives told the programme, speaking anonymously. "If it is him, he must have been brainwashed."
Morten Henriksen, a former neighbour of the family in Larvik, remembered Dhuhulow as a troubled teenager.
"He was pretty extreme, didn't like life in Norway… got into trouble, fights, his father was worried," Mr Henriksen said.
When the BBC showed him CCTV footage of the four Kenya attackers, he said that the one dressed in a black shirt and khaki trousers (pictured above) could have been Dhuhulow.
A family member, however, told VG, that they did not think the man in the video, or any of the other four men in the CCTV footage was their relative.
According to VG, a person named Hassan Abdi Dhuhulow was in March this year acquitted of murdering Somali journalist Hassan Yusuf Absuge in Mogadishu.
The PST, Norway's police intelligence agency, last week said it had sent officers to Kenya to investigate claims from Kenyan investigators that Dhuhulow had been involved.
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The attack on the mall began on Saturday 21 September, and lasted for four days. Kenyan police originally estimated that 10-15 terrorists were involved, but only four men have been seen in CCTV footage from inside the mall.
Norwegian media reported last week that the terrorist had made calls to Norway while the siege was been taking place.