On Monday, members of Parliament's code of conduct committee were due to start a probe into the incident, which left Woolfe in hospital last week.
The inquiry will be led by UK Tory MEP Sajjad Karim, who told this website, "As Chair of the committee we will need to secure all evidence including any CCTV footage as the incident happened within the Parliament building."
Witnesses to the incident, which happened on Thursday last week, will also be interviewed as part of the investigation.
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Karim added, "I would ask anyone with knowledge or evidence that may assist the investigation to contact the advisory committee secretariat."
According to a Parliament spokesperson, neither Woolfe nor Mike Hookem, the Ukip deputy who is alleged to have thrown the punch which landed Woofe in hospital, have made an official complaint.
However, press reports at the weekend said that Hookem had suggested he would take legal action against his colleague "if he continues to repeat lies."
Hookem told the Daily Mail newspaper that Woolfe was "acting" when he was pictured collapsed in parliament in Strasbourg.
Woolfe was discharged from hospital on Sunday three days after the incident.
Hookem suggested Woolfe, a contender to succeed Nigel Farage as party leader, may have staged a picture which showed him passed out.
He told the newspaper, "Now I'm not a medical man but that was pure Hollywood to me the way he was face down."
Ukip's former deputy Chair Suzanne Evans, also tipped as a leadership hopeful, branded the alleged brawl between the two men as "unseemly."
Ukip MEP Bill Etheridge, who lost the recent leadership contest to Diane James, also branded the row as "unseemly nonsense."