Spain international Asensio came on at half-time in Madrid's International Champions Cup meeting with Juventus at FedEx Field and spearheaded the attack, scoring twice in a 3-1 victory, FourFourTwo magazine reported.
With Los Blancos having sold their all-time leading goal scorer Cristiano Ronaldo to Juve and failed to add another central striker, despite links to the likes of Neymar and Robert Lewandowski, Lopetegui would be willing to use the 22-year-old in a new position this season.
"It's an option. Preseason is a time when we can test different things and what we need to do is look for resources or different ideas within the team," said Lopetegui.
"It was good to see him play at that position and he played extremely well. It's not important where he plays but how he plays."
Left-back Reguillon came off the bench against Manchester United last time out but played the full 90 minutes versus Juve.
Asked whether the 21-year-old Castilla defender could become a regular first-team player, Lopetegui said, "He's a young player with extremely strong abilities.
He has a lot of heart, effort and determination and I think he's working phenomenally with the club and ultimately it's a decision I'll have to take in the future."
A new goalkeeper is thought to be high on the list of Madrid's priorities ahead of the new La Liga campaign, with Chelsea's Thibaut Courtois said to be Real’s top target.
However, Lopetegui was unwilling to comment on potentially increasing the competition for the number one position.
"The day that a goalkeeper will potentially arrive I'll make a comment, but right now I want to talk about the great match that Keylor [Navas] had and also [Andriy] Lunin made his debut," he said.
"We obviously also have Kiko [Casilla] and Luca [Zidane], so I prefer to talk about the goalkeepers we have. If the day comes that there's another one, I'll answer you then."