Former Paris St-Germain boss Emery, who succeeds Arsene Wenger after 22 years, claimed success in 2018-19 would constitute "battling for every title".
Emery has added five signings but Kanu believes the Gunners, sixth last season, must be patient.
"If it happens and they win the league, it's a miracle," said the Nigerian.
"It takes time for the newcomers, the new signings, to adapt. We have to allow time for him to bring his own style and the way he wants to play."
Kanu helped Arsenal to two league titles during five years at the club and was part of the undefeated 'Invincibles' side of 2003-04.
Arsenal are yet to win the Premier League since then.
"For the new manager, it's going to be a very big challenge; the fans want them to perform in the league in his first year, which is always difficult for a new coach," Kanu said.
"It's a very big club - coming into a big club you need a trophy, so if you don't win the league, you need to win the others. It's hard, but that's what you expect of a coach of that stature and a big club."Emery has added Uruguay international Lucas Torreira for £26m, along with goalkeeper Bernd Leno from Bayer Leverkusen, defenders Stephan Lichtsteiner from Juventus and Sokratis Papastathopoulos from Borussia Dortmund, as well as 19-year-old midfielder Matteo Guendouzi from Lorient.
"He's been signing new, good players. They're more defensive, and not allowing goals, which is good," Kanu added.
"They have to know how to win games, even if it's 1-0. All they need is the three points."
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