The England right-back has been won over by the Portuguese from the outset. The defender predicted a successful campaign under Mourinho and said the extended summer break had left him in good physical shape after a difficult period marked by injuries.
Alexander-Arnold was forced to watch this summer's World Cup from home after Thomas Tuchel left him out of England's squad, a decision that drew criticism given his growing role at club level. He had to watch on television as England were eliminated by Argentina at the semi-final stage after Tuchel's side conceded twice in the closing stages having led for much of the second half.
The Liverpool-born full-back has been working at Valdebebas since the first day of pre-season this month.
"Everything's good. It's hot and there's a lot of intensity. We're in pre-season and that's what we expected. There are a lot of tough sessions, a lot of double sessions, so it's been intense so far," he said. "In summer you get a couple of weeks of rest and then a couple of weeks building back up your fitness.
"Now, in pre-season, you have to come back in shape. So I was ready and really looking forward to being back."
Alexander-Arnold also spoke about the impact Mourinho is already having on the group during his early days in charge.
"I've always admired the manager. I've played against him a couple of times and it's a pleasure to work with him and his staff. He's intense," he said, adding: "The principles and the demands are very high, so I'm looking forward to seeing that the more we get to know each other, the more we learn and the more he can teach us. And we're all willing and eager to learn and improve.
"I'm sure he'll teach us a lot of things and get us winning trophies this year," Alexander-Arnold predicted, ahead of a season in which Real Madrid will look to end a two-year wait for silverware. The club must first navigate a demanding pre-season before opening their LaLiga campaign away at Espanyol on Saturday 22 August.
"It's about getting ourselves fit, understanding the principles and how the manager wants us to play. Understanding how we're going to set up and present ourselves this season. And just getting fit and getting back into the action and getting the rhythm of football back.
"I've been out for a long time, so it's good to finally be back and lay good foundations for a successful season," he concluded, speaking to the club's official channels.