The Tottenham manager was speaking after Liverpool striker Luis Suarez was given an eight-match ban and fine of £40,000 for making racist remarks to Patrice Evra.
Redknapp is preparing his team to face Chelsea, whose captain, John Terry, has also been accused of making of racist comments.
But he denied the suggestion that racism was rife in England due to the mixture of ethnic groups present at each club.
When asked if he thought there was a problem with racism, Redknapp told reporters: "No I've never thought that, no. I don't know if there can be. You come into a dressing room, I've got as many black players here as white players so I don’t see where there should be a problem.
“They are all mates. They all play together, they all get on great together. It's not in my mind that those things happen anymore."
However, Redknapp did say that those found guilty of racism should receive the correct punishment for their actions, but he stopped short of passing comment on Suarez as he did not know what the Uruguayan was alleged to have said.
"There's no place for racism in sport or in life so I’ve got no time for it, and if somebody is definitely guilty then they have to take the consequences that's for sure, but I wouldn't be sitting here judging Suarez as I don't know what he said," he added.
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