Redknapp has signed a contract extension with Tottenham that ties him to the club until 2013.
The Tottenham manager's deal was due to expire next year but it included an option for a further two years which the club have now taken up following a successful season in the Barclays Premier League.
But the chase for 28-year-old Cole continues, with Redknapp hoping the former Chelsea midfielder will put football ahead of money when decision time arrives.
"I managed Joe before [at West Ham], and I signed him when he was 11," said Redknapp in an interview with Soccernet.
"We have always had a good relationship. I know what makes Joe tick and it's his love of the game, and his need to be playing it. That is what I am offering him."
Source: PA
Source: PA