Cesar has been linked with a loan move to Real Madrid following an injury to their goalkeeper Iker Casillas, while Nottingham Forest are reportedly targeting Green as a replacement for Lee Camp.
But both have proven their worth for Rangers in recent weeks, Cesar putting together a string of fine Premier League performances and Green keeping the club in the FA Cup with a brilliant display at West Brom.
And Redknapp said: "I don't want to sell Cesar or Green. They're two good quality keepers. They're our backbone. We need to keep them here.
"Cesar is a top keeper and you can understand why people would want him, but we've not had any enquiries."
Redknapp landed Loic Remy earlier this month, but a move for Yann M'Vila proved unsuccessful and Ryan Nelsen is leaving for the MLS at the start of February.
Further recruitment is the target and Redknapp admitted he is interested in South Korea defender Yun Suk Young, who will need to apply for a work permit.
He said: "I can't let anybody go unless we get some players in. We need to strengthen, not weaken the side and we have been trying.
"I haven't been home for 12 days. (My wife) Sandra said she'd forgotten what I look like. I said I look like Paul Newman. In my dreams!"