The Dutch side are currently on track to take their 34th Eredivisie title, and their accomplishments in Europe’s top club competition this season have been momentous after knocking out reigning champions Real Madrid and Juventus in back-to-back rounds.
The only slip-up that Ajax have encountered this season was their 6-2 home loss to Feyenoord, but this was avenged when they knocked the Rotterdam side out of the KNVB Cup with a 3-0 win.
Meanwhile, Spurs head into the first leg on Tuesday without their star striker Harry Kane, who suffered a season-ending ankle injury in the 1-0 first-leg victory over Manchester City in the previous round, while Heung-Min Son will also be absent through suspension.
Van Persie, who currently plays for Feyenoord, told Voetbal International: “When I played for Arsenal, Tottenham were the main rivals. At Feyenoord, Ajax are the main rivals. But that doesn't mean I can't be happy for those clubs. I have a lot of respect for Spurs and Ajax and the way they made it this far. I'd say Ajax are the favourites as Spurs are without Kane and Son.
"I reckon Spurs will be watching some footage of our league win over Ajax... Every game is different, but I thought we were the better team in the KNVB Beker game as well before the break. Things just didn't go our way."
Ajax have been the stand-outs of this season's Champions League thanks to key players such as Dusan Tadic and Matthijs de Ligt, who have been essential to the Dutch side's attack and defence respectively.
Fernando Llorente, who could step in for Kane in the first leg at the Tottenham Hotspur Stadium on Tuesday, believes this is an opportunity for him to show how he can help the team.
The striker told The Guardian: "It’s an amazing opportunity to give my best to help the team, to demonstrate I can help the team and I will try to do my best.”