Having been tipped to compete for the Premier League last term, United failed to live up to expectation during their first season under Mourinho.
The club struggled for consistency in the league, finishing on 69 points in sixth, but were still able to secure a return to the Champions League by clinching a first Europa League title last month.
Mourinho and his men are expected to mount a better title challenge for the 2017/18 season but first the side face an intense pre-season.
The Portuguese will be able to gauge his side’s development on the club’s tour to the US, which sees them play Real Madrid, Barcelona and Manchester City in the International Champions Cup.
They take on Champions League winners Real for a second time when they meet in the European Super Cup on August 8.
And Ferguson believes that these pre-season encounters will serve as fitting preparations for the club’s title challenge as Mourinho aims to become the first manager since the Scotsman to lift the Premier League trophy at United.
The 75-year-old made clear that Mourinho’s men have to be ready for the challenges ahead.
“The great thing about United is you’ve got to accept the challenge of beating the best,” he told ManUtd.com. “The expectation is always there and the matches we’ll face in the ICC are all big ones.
How Manchester United could line up next season
“It’s very good for the younger players to come into this type of competition in terms of preparing to be a Manchester United player.
“The more intense the challenge they can get, the better prepared they will be when facing Manchester City in an important league match or Real Madrid or Barcelona in Europe.
“The preparation to play in games as big as that can be started in pre-season tournaments like the ICC, which is fantastic.”