The 32-year-old's contract at Selhurst Park will run until the end of the current season.
Mathieu Flamini was released by Arsenal this summer.
Tottenham had a £12m bid rejected as the Eagles held their own in the summer window.
The England international's arrival would be 'icing on the cake' according to the Palace boss.
Benteke, 25, joined the Eagles on a club record £27m deal earlier this month.
Jack Wilshere will be allowed to leave Arsenal on loan on transfer deadline day.
Spurs had a £12m offer for Zaha rejected by the Eagles last week.
Remy reunites with his former Newcastle United coach Alan Pardew.
Spurs reportedly bid £15m for Wilfried Zaha on Thursday.
Tottenham Hotspur recently made a £12m bid for the highly-rated winger.
Zaha has informed Alan Pardew that he wants to leave Palace to join Tottenham.
Victor Wanyama scored his first goal for Tottenham Hotspur against Palace.
Christian Benteke joined Liverpool just last summer from Aston Villa for £32.5m.
Tottenham Hotspur host Crystal Palace at White Hart Lane on 20 August.
Liverpool striker is yet to agree personal terms but fee has been agreed.
The Belgian is set to have a medical at the London club.
Michel Vorm to deputise for injured Hugo Lloris.
Belgian is deemed surplus to requirements at Anfield.
The Eagles are keen to sign the Belgium international.
Crystal Palace also interested in signing 25-year-old Belgium international.
Belgium international does not figure in Jurgen Klopp's long-term plans.
The Eagles made it to the FA Cup final during the last campaign.