Barca's involvement in the latter stages of the 2019-20 Champions League means that they are late starters in the league this term, but Villarreal have also played twice in Spain's top flight, picking up four points.
Here, Sports Mole looks at how Koeman's side could line up at Camp Nou.
Barca will be without the services of Marc-Andre ter Stegen until at least the end of October with a knee problem, meaning that the club's number two goalkeeper Neto is set to start between the sticks.
Martin Braithwaite is also out with a thigh problem that he picked up in a practice match after the 1-0 win over Elche in the Joan Gamper Trophy last weekend, while Samuel Umtiti, who continues to be linked with a move away from the club, is unlikely to be involved due to a long-standing knee issue.
A new-look attack could include both Ansu Fati and Philippe Coutinho, with the former signing a new long-term deal at Camp Nou and the latter expected to be given the chance to make his mark under Koeman, having enjoyed a successful loan spell at Bayern Munich last term.
Luis Suarez's exit opens the door for Antoine Griezmann to start through the middle, with Lionel Messi expected to feature in a slightly withdrawn role. At one stage, Messi appeared certain to be leaving the Catalan giants, but the Argentine will spend at least one more season at Camp Nou.
Miralem Pjanic arrived at the club earlier this summer from Juventus, but a two-man midfield could include Sergio Busquets and Frenkie de Jong, while Nelson Semedo's exit means that Sergio Roberto will start at right-back.
Ousmane Dembele has been strongly linked with a move away this summer, but the France international now looks certain to remain at the club and should be on the bench for Sunday's contest.