Redknapp, giving evidence for a second day at London's Southwark Crown Court, denies tax evasion relating to $295,000 paid into the account when he was manager of Portsmouth.
The man tipped to become the next England manager, told journalist Rob Beasley from the now defunct News of the World that the payment was a bonus relating to the sale of England striker Peter Crouch to Aston Villa in 2002.
Beasley had been asking Redknapp about claims from former Portsmouth chairman Milan Mandaric that the money was for investments outside of football.
"I don't have to tell Mr Beasley the truth. I have to tell police the truth, not Mr Beasley, he's a News of the World reporter," Redknapp said, Britain's Press Association newsagency reported.
"I referred to it to him many times as my Crouch bonus," as "Crouch is an easy answer."
Redknapp added: "I just want to get Mr Beasley out the way - I just didn't want a story in the paper... I was going to come down to breakfast and all my players were going to be looking at the back page of the News of the World. It was going to be embarrassing."
Manchester United beat Tottenham on penalties in the 2009 League Cup final after a scoreless draw.
Mandaric, now Sheffield Wednesday chairman, is on trial along with Redknapp and also denies wrongdoing.
Redknapp named his Monaco bank account Rosie 47, combining his dog's name and his own year of birth.
Redknapp told the court he used the pet's name because "I loved her to bits."
