United are due to visit the US later this month, with a minimum of four games against strong opposition.
Following a clash with LA Galaxy, United take part in the International Champions Cup and will come up against Roma, Inter and Real Madrid.
Should they reach the final, United will take on Manchester City, Liverpool, Milan or Olympiacos, and Fletcher is looking forward to a tough build-up ahead of the 2014-15 season.
"You want to challenge yourself against the best and, although it's pre-season, if you're playing against someone like Real Madrid you are going to be against top-quality opposition," he told the club's official website.
"It's like in training here, when we play in two teams [in training] it becomes quite competitive and you'll see the same in these tour matches.
"Once you get on that pitch it's competitive and you always want to win every game and every tournament you're involved in.
"I'm sure the sports science lads will be saying that it's all about minutes and not getting injured but sometimes these games can get feisty.
"It's what you want as you want to make an impression and impress the fans and the manager because you want to be in the team for the start of the season."
