Redknapp has been manager of Portsmouth since December 2005
Those held included Portsmouth manager Harry Redknapp, the club's chief executive Peter Storrie and its former chairman Milan Mandaric.
The five men were arrested on suspicion of conspiracy to defraud and false accounting.
Mr Redknapp and three others have since been released on police bail. A 30-year-old remains in custody.
He is understood to be Charlton player and Senegalese international Amdy Faye, currently on loan to Rangers.
The City of London Police inquiry is believed to be centred around the transfer of Mr Faye to Portsmouth, a deal set up by agent Willie McKay.
Police refused to give details of those arrested and would only confirm they were aged 69, 60, 55, 48 and 30.
On-going inquiry
On his release Mr Redknapp said: "We all helped the police with their inquiries, but it doesn't directly concern me, it's other people involved.
"I've been answering questions to help the police. I am not directly concerned with their inquiries.
"They have to arrest you to talk to you, for you to be in the police station. I think that's the end of it, it didn't directly concern me."
The solicitor representing Mr Redknapp and Mr Storrie emphasised that his clients were cooperating with police.
Speaking outside the police station Paul Martin said: "The inquiries do not relate to either of those individuals, they relate to entirely different individuals.
'Corruption'
"They are ongoing investigations in relation to those other individuals, and for that reason they are unable to comment further, and there is nothing that they can discuss."
Meanwhile, a spokesman for Mr Mandaric confirmed that the Leicester City chairman was asked to assist police enquiries.
He said: "While the investigation remains on-going Mr Mandaric will continue to offer his full and total support to the police."
The arrests are part of City of London Police's on-going inquiry into alleged corruption, a spokesman said.
The men were held as officers carried out raids on 12 locations across the country. Two of those searches are still ongoing.
Detectives from the economic crime unit of the City of London Police are investigating allegations of corruption within football and its impact on owners and shareholders.
The club is fully supportive of Peter and Harry who are co-operating fully with City of London Police in this ongoing inquiry
Portsmouth FC
In July, officers raided Newcastle United, Portsmouth and Rangers football clubs as part of the inquiry.
A spokesman for Portsmouth said on Wednesday that the club's chief executive and manager had "been asked to help police with their inquiries concerning a matter dating back to 2003".
"This was prior to the new owner taking control of the club at the beginning of 2006," he said.
"The club is fully supportive of Peter and Harry who are co-operating fully with City of London Police in this ongoing inquiry.
"Both are playing major roles in the continued success of Portsmouth Football Club."
Seven arrests
Rangers FC have confirmed that a player was arrested in a matter "totally unrelated" to the club.
"It would be inappropriate to comment further," Rangers said in a statement.
Last year, the Premier League asked former Metropolitan Police Commissioner Lord Stevens and his company, Quest, to carry out a separate inquiry into several hundred player transfer deals.
In June, Lord Stevens presented his final report, which highlighted concerns over 17 transfers and five Premier League clubs.
City of London Police have distanced their investigation from Lord Stevens' inquiry.
The latest arrests bring the total number of people detained in connection with the investigation to seven.
In September, a 28-year-old man was arrested in London and in May, a 61-year-old man was arrested in Manchester on suspicion of money laundering.
Five men, including Harry Redknapp, the manager of the English football club Portsmouth, and former Portsmouh chairman Milan Mandaric (now at Leicester City) have been arrested by British police in an investigation into alleged corruption in British football transfers.  Reports suggest that they have been arrested on suspicion of conspiracy to defraud and false accounting

Portsmouth Chief Executive Peter Storrie and player Amdy Faye have also been arrested.