The veteran pair are off contract next month.
Pardew told the Croydon Advertiser: "Brede and Shola have played a major part - they haven't played much but behind the scenes they have been great. We have some great characters here, I want them to stay.
"Whether they agree with me about the valuations I think they should stay for is different. But Brede and Shola in particular haven't featured much but are fantastic characters.
"You couldn't ask for two better gentlemen to be around a young group of players. We're very lucky to have them."