Mourinho was confirmed as Real Madrid's new manager earlier this month, returning to the club for a second spell more than a decade after his first departure. The appointment follows Florentino Perez's re-election as club president.
Speaking to David Ibanez on El Desmarque from Montmelo, where he was attending the Spanish Grand Prix, the 23-year-old centre-back outlined his feelings about working under the Portuguese coach for the first time.
"With the new project, with Mourinho, I think it's very exciting and I'm looking forward to getting started."
Asencio, a graduate of Real Madrid's youth academy, shared memories of Mourinho's first spell in charge of the club between 2010 and 2013, a period he followed closely as a young supporter.
"I was young and I watched it, how he changed the team, the competitiveness he brought to the club, the fight and the grit. I think those are characteristics that suit me as a player."
Mourinho's first stint at the Santiago Bernabeu remains best remembered for the 2011-12 LaLiga title, secured with a then-record 100 points and 121 goals scored across the campaign. Asked whether a repeat was realistic under the same manager, Asencio was unequivocal.
"Can the league be won next year with Mourinho? Yes, of course. He did the record-breaking one. Let's go for it."
The defender also addressed speculation linking Manchester City midfielder Bernardo Silva with a move to the Santiago Bernabeu as part of Mourinho's rebuilding plans. Asencio was complimentary about the Portugal international's qualities.
"Bernardo Silva is very, very good, it would be a step up in quality for the team."
He added that the squad would welcome any incoming signings with open arms, expressing confidence in the direction the club's hierarchy is taking.
"Whatever comes, we'll receive it with open arms and we're sure that the project they're building is incredible."
The comments come during a summer of significant upheaval at Real Madrid, with the club already moving on multiple fronts to reshape the squad around Mourinho's demands. For a young defender like Asencio, who has come through the club's academy system, the prospect of working under a coach whose previous spell delivered a record-breaking title represents both an opportunity and a clear marker of the standards now expected.
With pre-season still some weeks away, Asencio's comments offer an early sense of how the dressing room is responding to the appointment, suggesting at least among the squad's younger players, the changes being made at boardroom level are being met with enthusiasm rather than uncertainty.