According to a report in The Daily Telegraph, the man, said to be in his 40s, was interviewed under caution by Scotland Yard in June following a complaint linked to an incident at a pub in south-west London's SW6 district, which includes Fulham and Parsons Green.
Chelsea have released a statement urging fans travelling to Stamford Bridge for their English Premier League match against Arsenal on Sunday to take extra precautions in the aftermath of Friday's terrorism incident in London, as Parsons Green is near the club's stadium.
The incident took place at the Parsons Green station, which has been closed.
British Prime Minister Theresa May said military personnel would replace armed police "on guard duties at certain protected sites which are not accessible to the public".
The total number of arrests in the case has increased to six.
Earlier, an 18-year-old man was arrested in the port area of Dover. None of the suspects have been named.
Friday's explosion on the London tube is the latest in a string of terror attacks in the United Kingdom in recent years. Here is a timeline of the terror that has unfolded in the UK.
Scotland Yard's Counter-Terrorism Command investigating the attack arrested the 25-year-old from Newport.
"I never think it's helpful for anybody to speculate on what is an ongoing investigation," May said.