Erik ten Hag's side posses some of the most revered young players in Europe and are enjoying a revival after four successive runners-up finishes in the Eredivisie.
Paired with defending champions Real in the first knock-out round of Europe's premier club competition, the Dutch side are naturally the underdogs but Sneijder is hopeful of an upset.
"I don't see Real Madrid as being as strong as in previous years. That's obvious.
"Ajax are a very young team, but nobody should be mistaken about them as they have a lot of quality and play very well, especially at home in Amsterdam.
"It'll be a difficult tie for Real Madrid."
Los Blancos have endured a contrasting campaign, replacing Julen Lopetegui with Santiago Solari after a poor start to the season.
Solari guided Real to the Fifa Club World Cup earlier this month but there remain questions over his long-term future.
Ajax's last progressed beyond the round-of-16 in the 1995-96, when they beat Real en route to the final - where they lost to Juventus on penalties.
Sneijder, who played in Amsterdam between 2002 and 2007 before moving to the Spanish capital for two seasons, says the two-legged tie will be a decent barometer of progress made by his boyhood club.
"Real Madrid are still the favourites despite everything," he added.
"But look! If Ajax can achieve a good result in the first leg then Real Madrid could have problems, and we've seen that recently when they face teams that keep the ball.
"This is a good matchup to check the quality of this Ajax side, one that is very exciting, as they go up against the three-in-a-row Champions League winners.
"Real Madrid are different in Europe, but Ajax have a chance to move on to the next round."
"They believe that Ajax are the same as the last few times they visited Madrid. But they're nothing like those teams.
"Plus, the average Real Madrid fan doesn't follow Dutch football and doesn't know about Ajax.
"I do know about them, though, and they have a line-up with a lot of quality."