Mauricio Pochettino's side are currently out of the Champions League places, although they can draw level on points with fourth-placed Liverpool if they win at Wembley and overtake Jurgen Klopp's side if they beat the Toffees by five goals or more.
But the club have a new 61,500-seat stadium to pay for at a time when rivals with deeper pockets are eyeing some of their top performers. Top scorer Kane is reportedly coveted by Real Madrid and the Champions League holders have also been linked with midfielder Alli, along with Paris Saint-Germain. Left-back Danny Rose is believed to be a target for Manchester United.
But Levy has made it clear that the current window is a time for squad-strengthening, not weakening, and said he would reject any unwanted offers in the summer as well.
"I'm 100 per cent confident," he said. "Every single player that we want to keep, I can assure you will be playing for Tottenham Hotspur next season.
"Mauricio's strategy has always been that if an opportunity arises that he thinks can improve the squad then we will need to look at it, but January is always a very difficult window."
Levy is in negotiations with Alli over a new contract that would bring him roughly into line with the money paid to Kane, who is Tottenham's highest earner and who may be granted a contract upgrade himself soon. Midfielder Harry Winks is a doubt against Everton because of an ankle injury, Rose is set to miss out because of a knee problem while centre-back Toby Alderweireld is working his way towards a comeback from a hamstring tear sustained in early November.
The encouraging start to Sam Allardyce's reign as Everton manager has faded in recent weeks. The Toffees have not won in five matches and are out of the FA Cup following a painful third-round defeat at Liverpool last week.
Defender Mason Holgate was involved in a confrontation with Roberto Firmino at Anfield that could have consequences for both players. Having claimed he was racially abused by the Liverpool striker, Holgate himself is reportedly facing the prospect of Football Association action for alleged homophobic tweets sent from a now-deleted Twitter account more than five years ago.
There is better news elsewhere for Allardyce, with right-back Seamus Coleman back in training after nine months out with a broken leg and Turkey striker Cenk Tosun set for his debut after completing his ?27 million ($36 million, 30 million euros) move from Besiktas.
Captain Phil Jagielka has acknowledged that Everton have to be better in attack, saying: "The gaffer does not say to us that the be all and end all is to defend and we forget about going forward.
"He wants us to cause problems for the teams we play against. It is up to us to find a mixture of both defensive resolve and attacking purpose."