The duo has long been linked with a move away from Palermo.
Manchester United, Manchester City and Inter Milan have all been linked with a move for Kjaer, while City and Wolfsburg have targeted Cavani.
“Tottenham have bid €35m, an offer we cannot refuse, seeing as the two players have both said they want to leave,” Zamparini told Sky Italia television.
“We will reinvest the money for these players,” assured Zamparini. “The midfield is my biggest concern, whereas in defence and attack we are fairly covered.”