Klopp's Liverpool travel to Molineux for the Premier League's weekend opener early on Saturday.
Nunez started up front in both of Uruguay's World Cup qualifiers this week, but was taken off at half time in their defeat to Ecuador.
Uruguay manager Marcelo Bielsa told the media post-match that Nunez was taken off due to a muscular discomfort.
Bielsa added that Nunez's inability to keep up with the team's press due to the lingering issue was the reason behind his early substitution.
That will give Klopp a decision to make, given that Liverpool's aggressive style of play is centred largely around high pressing.
Nunez was brought into the starting XI against Aston Villa after netting twice off the bench in the Reds' 2-1 win at Newcastle United, replacing Cody Gakpo.
Gakpo would likely be the most suitable candidate to come back in, and he hit form for the Netherlands, scoring in both of Oranje's Euro 2024 qualifiers this week.
Diogo Jota was also on the scoresheet for Portugal to stake his claim for a start, notching two of Portugal's nine in their dominant 9-0 thrashing of Luxembourg.
On top of Nunez's injury though, Liverpool had three other players on international duty in South America this week.
The fitness of Alisson Becker, Alexis Mac Allister and Luis Diaz will also be assessed after the trio were all on duty on Tuesday night in CONMEBOL World Cup qualifying.
In recent years, it has not been uncommon to see players only start on the bench after returning late from international commitments on the continent.
Losing another three players from the start at least
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