According to the OP, I'm free to choose a formation of my own choosing. I chose to interpret that as I'm free to pick my own system. In which case, I've decided to create what is in my view, an upgraded version of Roberto De Zerbi's Sassuolo.
First and foremost, it was important to identify full backs that would be reliable for ball retention in the build up phase. A full back that makes several assists in the course of a season wasn't quite what I was looking for, nor a player that makes an overwhelming amount of crosses which rules out the likes of Alexander Arnold. I didn't quite want full backs masquerading as wingers. For this reason, I've gone with Leeds' captain, Luke Ayling. Instead of operating as a winger, he's very much integral to the build up phase by being a playmaker in the first phase in the build up. Sassuolo have a patient and sustained build up, utilising the full backs in deep areas. In the case of Liverpool, the full backs are quick to make long balls over the top to the likes of Mane, and Salah. I'm looking for a more patient approach especially since playing centrally is a key part of Sassuolo's playstyle whereas Liverpool have a strong emphasis on creating from the full backs and relying on the offensive quality of their attacking trident. The experience of playing in Biesla's system is why I've given Ayling the nod here. The other full back I'd choose is Alex Sandro. I struggle to think of a full back better at getting out of tight situations deep into ones own territory. He's also a very capable passer from deep areas. Therefore, I think he would adapt well to the role I have in store for him.
In central defence I wanted two ball playing defenders as Sassuolo patiently work their way to get a spare man on the ball capable of making a progressive pass. The name that immediately stood out to me for this purpose is Alaba. I haven't seen a CB more gifted on the ball than him. For the right side of defence, I wanted someone that actually plays on the right side which rules out the likes of Ramos and Van Dijk. For this reason, I went with Pique whose used to taking responsibility on the ball. He also has the confidence, and personality required for the role. Behind the sticks, Ter Stegen I wanted a keeper that maintains his composure when the team is being pressed, as well as having the technical ability to make passes which breaks lines.
My answer to Locatelli from Sassuolo's midfield is K.Phillips due to his role in Biesla's system. Similar players in my view. Partner in midfield is Verratti due to his experience, ability on the ball when pressed, as well as his demeanour and personality. On the occasions I watched Sassuolo, I never quite got the feeling that the advanced midfielder Djurcic is the heartbeat of every attack like say a De Bruyne is for Man City. Djurcic is also has a very slight figure, as opposed to having that robustness of a KDB or Muller. Therefore, the player I've gone for is Di Maria. Slight figure, but highly technical, and plays in a system which the burden of creativity isn't heavily placed on his shoulders.
On the left, Sassuolo play with Boga who has one of the highest volumes of successful dribbles in Europe. In my attempt to adopt a somewhat similar team to Sassuolo, there was no other option than Neymar whose one of the most prolific dribblers in Europe. However, he'll be resigned to a role closer to that of Barcelona where he stretched the pitch as opposed to the freedom he gets with Tuchel. On the right it was important to have a left footed player that can stretch the pitch, plays in a system which he himself is prolific, and plays in a system where the main #9 is also prolific. That rules out the likes of Salah who has Firmino playing a sacrificial role. In contrast, Mahrez managed to get very respectable numbers in a team which Aguero and Jesus are prolific themselves. The two highest scorers in the Sassuolo side is the right inside forward and number nine respectively.
Speaking of number nine, looking at the top 10 scorers in Europe's top 5 leagues the players which Caputo is more comparable with, in terms of individual skillet (peeling on the last man) is similar to that of Aubameyang, Ings, and Vardy. So that rules out the likes of Lewandowski. Given that Caputo managed to have around 6 assists, the option I've gone out of the three is Vardy.