The No.66 has moved inside to a more central position on the pitch during the Reds' fixtures with Arsenal and Leeds United, having started in his familiar right-back berth on both occasions.
The switch has so far been successful, with Alexander-Arnold claiming three assists in those games and earning the Carlsberg Player of the Match accolade for his performance at Elland Road in the 6-1 win on Monday night.
Asked during his pre-Nottingham Forest press conference whether this could now be considered the 24-year-old's position moving forward, Klopp replied: "We will see that. Trent, in each position he plays for us, is always a super-important player.
"This slightly advanced role now suits him in the moment really well, that's good. It's a challenge for everybody else to cover the spaces when we lose the ball theoretically, but with him there we didn't lose that many balls, which was helpful.
"That's it pretty much, but it's not written in stone or whatever – why should we? He can play in different ways and how he played the last two games was really, really good, that's true."
Klopp explained the considerations required before moving Alexander-Arnold into the position, such as the impact on the players around him, particularly in defensive situations.
The manager added: "Trent is a smart player, but it is much more about how we set it up around than that Trent can play the position – we were never in doubt, but you have to set it up around that then because there are moments when we lose the ball we have a different position.
"Where is Robbo in these moments? Where are Virgil and Ibou in these moments? These kind of things. How do we get him on the ball, because that's obviously important.
"We sit here and talk about it and maybe we do it like this tomorrow [against Forest] or not, we will see, but if Trent shows up there, maybe he gets a man-marker, that's possible, and then doesn't get the ball, then we have to deal with that and these kind of things.
"It's now not the solution for all the football problems we had this year, but he has the potential to play that position. That was always clear, but especially in the way we do it now with defending on the right-back and offensively being there. That's absolutely fine and we will see where it leads to."