In an interview with Dutch website Wielerflits, Contador, who retired at the end of 2018, also spoke about another young talent, Remco Evenepoel, revealing the Belgian was putting out Grand Tour-winning numbers as a junior.
Van der Poel has taken the sport by storm, winning the cyclo-cross world title three times, as well as a string of mountain bike successes and, more recently, a number of victories on the road.
In his debut spring classics campaign last year, he won Amstel Gold Race in dramatic fashion and also triumphed at Dwars door Vlaanderen and Brabantse Pijl, as well as finishing fourth in his first Tour of Flanders.
The 24-year-old has not been afraid to attack early and open up the races, which has struck a chord with Contador, who always placed an emphasis on putting on a show.
"Van der Poel now is maybe a little bit like Messi. Why? Because maybe you don't support FC Barcelona, but if you have the opportunity, you go there to watch Messi play," Contador said.
"With Van der Poel, you go to a race, and maybe it's a very small race, but people watch the race to watch Mathieu van der Poel. This is incredible."
Van der Poel is still in the early stages of his career, with much guesswork as to what he might go on to achieve. In the short term, after collecting his third cyclo-cross world title last week, he will target the Spring Classics on the road, including Paris-Roubaix, before switching to mountain biking for the Olympic Games. After that, he hopes to make his Grand Tour debut at the Vuelta a España.
Contador played down suggestions that Van der Poel might be able to challenge for a Grand Tour title in the future.
"Sometimes we are crazy, saying ‘maybe he can win the Tour, or whatever’. There are some riders that do something incredible, like Peter Sagan, [and people say] 'maybe if Peter lost weight...' but Peter Sagan is Peter Sagan. Peter Sagan can take one shoe out of the pedal, but it back in and win.
"Van der Poel can attack and put five seconds into other sprinters. Riders who finish second feel like they've won, because they're behind Van der Poel. In my opinion, it's important that we are clear he's doing something incredible, that we enjoy his victories, and that he continues with his performances and progression."
Contador was also asked by Wielerflits about another of the sport's young stars, Evenepoel, who skipped the U23 ranks to turn pro with Deceuninck-QuickStep in 2019 after winning the road race-time trial double at the junior World Championships.
His debut season was remarkable, with victories at the Clásica San Sebastián and elite European time trial championship, along with a podium in the elite Worlds time trial, and 2020 has already seen victory at the Vuelta a San Juan, a result that saw locals also compare him to Messi.
"He’s super class," said Contador. "He’s a rider that has the numbers to win a Grand Tour. I was speaking to him last year before the start of the season, he told me the numbers in his tests before the junior World Championships, and they are numbers to fight for victory at Grand Tours.
"In my opinion, Remco is strong in the Classics, but he's also a rider with big potential for the Grand Tours. Of course, we need to see if he recovers well stage-by-stage, and arrives strong in the third week. But in terms of watts-per-kilo to fight for Grand Tours, he has that."