O'Neil, who was back in action in Saturday's 3-1 win over Bolton after his summer ankle operation, has been linked with a move to Middlesbrough as part of a reported bid to bring striker Yakubu Aiyegbeni back to Fratton Park.
Taylor, who fired home Pompey's third goal against Bolton from the penalty spot, has been the subject of speculation over a possible switch to Tottenham.
But Redknapp said: "I saw something in the paper which said I'd offered money and Gary for Yakubu, about £10million-plus, but I don't know where that came from.
"I've never offered Gary O'Neil to anybody. It's nonsense. Nor Matty Taylor.
"They are two lads who are here. I want to keep two of my best players."