Redknapp is a huge admirer of the Hammers ace, and a replacement for long-term absentee Tom Huddlestone is top of his new year transfer plans, but an offer for Parker won't be forthcoming.
The Tottenham chief, who has taken his side into the first knockout stage of the Champions League, will instead have to find a younger alternative to satisfy his chairman Daniel Levy.
"I like Parker, but he belongs to West Ham," Redknapp said. "He will be 31 next birthday and they will want £15million. Daniel wouldn't buy players of that age, on big wages with no sell-on."
A more likely transaction between the two clubs would be a deal for Jamie O'Hara, whom Avram Grant worked with previously at Portsmouth.
He appears to have no future at White Hart Lane and the former Hammers boss now seems prepared to let him go.
Redknapp added: "O'Hara needs to play. He would be better off playing somewhere than not playing. He would do a good job for someone in the Premier League."