Mauricio Pochettino's side could win the Champions League next week when they face Liverpool in the final after knocking Ajax out in the semi-finals, but that might not be enough to lure Europe's best players to north London.
Spurs have been linked with a move for Youri Tielemans, who has performed well on loan at Leicester, but Anderton believes his former club should instead opt for Van de Beek, who helped Ajax reach the semi-finals of the Champions League for the first time since 1997.
Anderton told Sportingbet : "Tielemans had a good half season at Leicester but Tottenham should look to sign Ajax’s Van de Beek over the Belgian. He was excellent in both legs against Tottenham and would be a great signing for the club. He’s a different class to the other players Tottenham have been linked with and the one I think they need to sign ahead of anyone else.
"Tottenham’s wage structure means that regardless of whether they win the Champions League or not, they won’t be able to sign Europe’s top talent. I think that Alderweireld is the one player that has already made his decision and he won’t be at the club next season.
"At the end of the day, the very top players are going to want top money and Spurs don’t pay what United, City, Liverpool and Chelsea do. There is always going to be an issue with certain players, because whether they admit it or not they are always going to want as much money as they can get, regardless of how ridiculous all the money being thrown around is at the moment.
"If Tottenham do win the Champions League, it would make it more difficult for the likes of Eriksen and Vertonghen to walk out the door, but at the end of the day, money talks. Tottenham have an incredible stadium and an incredible manager in Pochettino. If you are a player looking in from afar, I would like to think it is a team that most players would love to come be part of and make a difference and help Tottenham challenge consistently.
"Tottenham have everything set up to go and be a top team for the next decade, but if they aren’t able to offer the big money to accompany the stadium and the manager, it’s going to be very difficult to attract the top players and keep hold of their stars."
"Once the likes of Real Madrid and Barcelona’s declare an interest in him, it’s going to be difficult for Tottenham to compete with them,” added Anderton.
“At some point in a player’s career they are going to want to play at one of those clubs, it’s natural. He is a loyal guy, so it wouldn’t surprise me if he does stay but it’s far from a formality."
However, while Anderton is an admirer of both players, he does not believe they would currently make into Spurs’ best starting line-up.
He said: "Jack Grealish wouldn’t improve Tottenham’s team and they’ve got better players in his position already. We’ve seen from his performances for Aston Villa this season that he's a very talented player but he isn’t good enough to walk straight into their starting team.
"Grealish certainly has the potential to develop into a top, top player and he would fit the Spurs ethos, but if he joins it would very much be as a squad player.
"Wilfried Zaha wouldn’t get in Tottenham’s starting team and he would be too expensive to sit on the bench. There’s no doubting he is an excellent player but I don’t see him coming into the Tottenham team and replacing the likes of Son, Eriksen, Alli or Kane.
"He’s has got a little bit of arrogance, swagger and a real belief in his ability, but he would be a hell of a lot of money to spend on someone who is not going to walk straight into the team. If he was to come in as a squad player, he would be an incredible addition."