The television presenter was stabbed several times near his house in Wimbledon on Friday and is now said to be recovering from his injuries in hospital.
A witness said that two young men sprinted away from his body in Queensmere Road and were laughing as they then fled the scene in a car.
Mr Zeraati was photographed in the hospital giving the peace sign on Saturday and could be discharged soon.
The Metropolitan Police is investigating but has not yet made any arrests.
The 36-year-old presents a show on the Persian language network Iran International and responders said he was shouting that he was a journalist at the point of the stabbing.
However, Iranian charge d’affaires in London Mehdi Hosseini Matin said there is no link, the Guardian reported on Sunday.
“[There is] no link to this story of this so-called journalist,” Mr Matin tweeted. He added that the media had tied the two together “without evidence” and that it was “strange and questionable”.
Iran International said on its own website: “It is still unclear who the attackers were and what their motive was.
“But fingers were pointed at the Iranian regime almost immediately after the news broke, given the Islamic Republic’s track record in plotting against dissidents – and even foreign officials.”
Hannah Neumann, a Green member of the European parliament, tweeted: “We all need to urgently do our homework to protect those who seek refuge here from transnational threats and violence.”
