European champions Portugal are level with Spain on four points at the top of Group B and need a draw to guarantee qualification.
Iran, who beat Morocco in their opening game before losing to Spain, are trying to reach the latter stages of the World Cup for the first time.
“We’ve seen all the qualifying games, not just those at the World Cup, and we’ve seen they’re a very organised team,” Santos said on Sunday.
“They have quality players, with the experience of two successive World Cups and some of them are playing in big leagues like Spain, Greece or Russia.”
Iran must win in Saransk to prolong their Russian adventure and will take heart from a narrow 1-0 loss against Spain, a game decided by a fluke Diego Costa strike.
“In my opinion they are the best Asian team,” Santos said.
“They have a lot of ability as a team and not just as a defensive team. They also know how to play on the counter as they showed against Spain.
“We have to prepare ourselves for a tough battle, with two teams that want to win and that are going to do everything to achieve that.”
Portugal go into the contest as heavy favourites to progress, but veteran centre-back Pepe strongly insisted the job was not yet complete.
“We don’t think we have a foot and a half in the last 16 and this is a good thing,” Pepe said.
“We have a lot of respect for our rivals and it’s a very important game because it’s going to give us the chance to get through the group phase.”
Cristiano Ronaldo has scored all four of Portugal’s goals so far in the tournament, although Santos rejected suggestions the team is overly reliant on the five-time Ballon d’Or winner.
“He makes the difference here, like he does at Real Madrid and before at Manchester United and Sporting Lisbon,” Santos said. “But on Monday Iran are going to play against Portugal, not against Cristiano.”
There will be a familiar face in the Iran dugout in Carlos Queiroz, a long-time friend of Santos’s who coached his native Portugal at the 2010 World Cup.
The former Real Madrid boss and Manchester United assistant has been in charge of the Iran national side since 2011.
Queiroz admitted it would be “a special day” facing his homeland but said friendships would be put to one side as he bids to make history with Iran.
“We have to be realistic, we’re going to play against one of the strongest teams at the moment, Queiroz said.
“Portugal are not only a contender, they’re one of the favourites for the title.”