Mourinho led United to victory in the League Cup and Europa League last season, the latter yielding a place in the Champions League, but their football was drab and they finished a distant sixth in the league.
Having won the league in his second season in his last five jobs — Porto, Chelsea (twice), Inter Milan and Real Madrid — he will be expected to mount a strong title challenge at the very least.
“Can we win it? We can, but maybe we won’t,” Mourinho told ESPN in a recent interview.
“Everything is good and strong, but some of them (other clubs) are really strong in the market, so it is going to be difficult.
“Normally the second season should be better than the first because you know the club, you know the players. The players, they know you.
“The club know you can affect in a positive way the structure, you can affect in a positive way the people that work around you.
“But this is modern football. It’s getting much harder for everyone, so we don’t know.”
United’s signings have been thoroughly in keeping with Mourinho’s pragmatic approach to the game, the Portuguese having galvanised his squad with extra height and muscle.
Centre-back Victor Lindelof, midfielder Nemanja Matic and striker Romelu Lukaku are all over six feet (183cm) tall, giving United the second-tallest squad in the division behind Tony Pulis’s West Bromwich Albion.
Lukaku faces the greatest scrutiny, having been brought in to replace Zlatan Ibrahimovic after the charismatic Swede was released in the wake of the serious knee injury he suffered last season.
Lukaku, 24, has scored 87 goals for Everton over the past four seasons, statistics that moved United to sanction a £75 million ($97.9 million, 82.9 million euros) acquisition.
– Make-or-break for Martial –
But the Belgium international failed to convince Mourinho during their time together at Chelsea and will be playing in the Champions League proper for the first time.
A battering-ram striker in the finest Mourinho traditions, Lukaku’s task is to sharpen an attack that mustered only 54 league goals last season.
“I’m here to score goals and be the focal point of the team,” Lukaku said.
“At Manchester United, we play to win and that’s the mentality when I get on the pitch.
“I’ve been waiting for this opportunity. Now I’m here and it’s time to work hard and, hopefully, deliver.”
With Ibrahimovic and Wayne Rooney no longer around, there is pressure on Paul Pogba to establish himself as the team’s leader after blowing hot and cold in his first season following his return from Juventus.
Anthony Martial, meanwhile, faces a make-or-break campaign, having slipped from view last season after failing to earn Mourinho’s trust.
The 21-year-old Frenchman faces stiff competition for one of the two or three places in support of Lukaku, with Marcus Rashford, Henrikh Mkhitaryan, Juan Mata and Jesse Lingard among Mourinho’s other options.
Matic, who won the league with Mourinho at Chelsea in 2015, is expected to slot into midfield alongside Pogba and Ander Herrera, with former Benfica man Lindelof due to partner Eric Bailly at centre-back.
United face a relatively benign start to the season, Rooney’s return to Old Trafford with big-spending Everton the most taxing assignment of their opening seven fixtures.
But October and November bring meetings with Liverpool, Tottenham Hotspur and Chelsea in the space of three weeks, by which time United’s Champions League campaign will be in full swing.