The Tottenham manager "voluntarily" revealed details about his Monaco bank account during interviews with the Quest inquiry in 2006, top accountant Nigel Layton said at Southwark Crown Court.
Redknapp told Layton "I don't care who looks" as Portsmouth were looked into by the investigation led by former Metropolitan Police commissioner Lord Stevens.
It is alleged Redknapp said: "A friend said to me, he said 'Harry, I can't believe it's always you, I have dealt with you enough times. Your problem is your name, Harry, and you have got a Cockney accent'.
"People don't know me and I am sick and tired of it.
"There ain't nobody who is more of a fan... My son has been a top footballer.
"If there is any mud to be thrown, I seem to get on the end of it for whatever reason."
Southwark Crown Court heard transcripts of a conversation which took place between Layton - managing director of Quest - and Redknapp in November 2006.
Redknapp added: "I don't care who looks, your people can look. Nobody will ever find anything on me. I don't care who looks or how hard because there is nothing on me in this world."
Layton and other officials from Quest met Redknapp several times after first talking to Portsmouth executives, including Milan Mandaric and then-chief executive Peter Storrie, in May 2006.
Under cross-examination by Redknapp's lawyer John Kelsey-Fry QC, the financial executive said the manager was "forthcoming" in telling the inquiry about his Monaco account.
"Quest had no power whatsoever to order the disclosure. All we could do was ask for the disclosure," Mr Layton said.
"In this instance, voluntary disclosure was forthcoming."
Redknapp, 64, and Mandaric, 73, deny two counts of cheating the public revenue.
Jurors were also asked to consider how the Spurs boss "simply laughed" when questioned about the Monaco "bung".
Prosecutor John Black QC completed his opening speech by pointing out how Redknapp's story differed from co-defendant Mandaric's.
"Those explanations, the Crown say, are contradictory, inconsistent and lack credibility," Black said.
Black said: "At the heart of the Crown's case is the fact that no tax was paid."
Both payments were employment related and were therefore taxable, Black added.
"You may think in this case there can be no doubt that these payments constitute bonus payments paid while he was manager at Portsmouth," Black told Southwark Crown Court.
Mandaric was determined to "maintain the goodwill" of a talented manager, Black added.
"He was a prime candidate to be poached by other clubs and in the event that was what transpired," the barrister added.
Jurors were asked to consider, "is it credible that Mr Redknapp remained blissfully unaware" of the deposits in the account named after his pet dog, Rosie.
Black also pointed to evidence that Redknapp "simply laughed about it and decided to forget about it all".
Referring to police interviews with Mandaric, Black asked "is there any credibility, you might like to consider" that the payments "constituted a loan".
Black said: "Why, in that case, was Mr Redknapp under such misapprehension?"
Redknapp claimed he "received express reassurances from Mr Mandaric that the tax had been paid", while Mandaric "assumed that Mr Redknapp would take legal advice and make the necessary action".
Both Redknapp and Mandaric deny two counts of cheating the public revenue when Redknapp was manager of Portsmouth Football Club.
The first charge of cheating the public revenue alleges that between April 1, 2002 and November 28, 2007 Mandaric paid 145,000 US dollars (£93,100) into the account.
The second charge for the same offence relates to a sum of 150,000 US dollars (£96,300) allegedly paid between May 1, 2004 and November 28, 2007.
