Tottenham and Liverpool were both said to be close to signing the young striker before he went to the Stadium of Light for a fee of £8million that could rise to £12million.
"We kept looking at him. We watched him dozens of times and we liked him but we felt it was a lot of money for him," Redknapp said.
"We have young players here like Harry Kane. He is a bit younger, we like him and we didn't feel we wanted to pay that money for Wickham."