Flamur “Alex” Beqiri, 36, was killed in front of his family near their £1.5million townhouse in Battersea on Tuesday.
Mail Online reported Mr Beqiri - the brother of former Real Housewives Of Cheshire star Misse Beqiri - was wanted by Swedish police in 2008 amid claims he was part of a drug smuggling ring pushing cannabis into Scandinavia.
The site reported drug charges against him were later dropped.
A report in Expressen, a national Swedish newspaper, in 2007 said the then 24-year-old Beqiri was wanted after 340kg of cannabis was seized by customs officials.
Expressen also reported yesterday that Beqiri was a close friend of Karolin Hakim, a female physician who was shot dead in Malmo in August this year, and that the latest killing could be linked to criminal gangs.
No arrests had been made as the Met Police continued its murder investigation on Friday.
Mr Beqiri had been returning home from a night out with his wife and young child when he was gunned down. Witnesses said there were up to 10 shots.
Det Ch Insp Jamie Stevenson said on Thursday that the force was working to establish the motive. Mr Beqiri’s family are receiving specialist support.
Mr Beqiri is reported to have married his wife, Debora Krasniqi, in Cernobbio by Lake Como, Italy, in October last year.
An article in Grace Ormonde Wedding Style magazine, which published photos of the occasion, revealed the couple first met through Facebook.
Ms Krasniqi told the magazine that the pair, initially just friends, “fell deeply in love” at his sister’s wedding after speaking for “endless hours over the phone”.
“There was always something special about our connection and bond,” she said.
Neighbours living near the scene of the shooting described hearing multiple gunshots followed by a woman screaming “desperately” for help.
Vittoria Amati, 60, said she heard between “eight to 10” gunshots fired in quick succession.
Mrs Amati told PA: “I then heard the screams of the wife. I came out and realised it was one of my neighbours.
“He was lying in front of his doorway in a pool of blood. He was still alive. We were really hoping he would make it.
“You have no idea how desperate she (his wife) sounded.”
The death is the 142nd homicide in the capital in 2019, the highest number in a calendar year since 2008.
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Last year, there were 141 police-recorded homicides in London, according to Home Office statistics.
Additional reporting by PA.