The two faced each other in the Premier League in August and Rose and Spurs were the winners, as they secured a 1-0 victory thanks to a late goal from Victor Wanyama.
Rose joined Spurs from Leeds as a teenager before progressing through the North London academy and has gone on to make 126 appearances.
Rose is one of a number of players to graduate from the Spurs academy that has also produced Harry Kane, Ryan Mason, Tom Carroll, Nabil Bentaleb and Josh Onomah as well as Andros Townsend, who joined Newcastle in January before joining Palace in the summer.
In other Tottenham transfer news, Ledley King names three qualities in the squad after window closure.