The London Evening Standard says his current salary of £75,000-a-week is a stumbling block for Alan Pardew's side, while the forward also faces an uncertain future due to being bailed until September over a rape allegation - which he denies.
Remy has reported for pre-season training as planned and Redknapp admits that he is hoping the 26-year-old will help his bid to win promotion back to the Premier League.
He said: "I wouldn't want to get rid of Remy. He is a top player. He would be fantastic for us next season. If I can keep hold of him, I will do."