Head coach Andoni Iraola confirmed the latest setbacks after both players were forced off during Liverpool's 2-1 Premier League victory over Brentford on Saturday.
Frimpong's injury is particularly frustrating, with the right-back struggling to maintain fitness since joining Liverpool from Bayer Leverkusen last year.
"Frimpong has a new muscle injury. Difficult to predict. We will have to wait until he recovers, but it is going to be difficult before the international break," Iraola said on Monday.
The November 9-17 international break could therefore come too soon for the Netherlands international, who has endured a difficult period trying to establish himself at Liverpool.
Szoboszlai's situation is more encouraging, with Iraola insisting that the midfielder has not suffered a new injury but has experienced a recurrence of the problem that previously kept him out of action.
"Szoboszlai is different, it's not a new injury. I think it is in the same place it was in the past week. It hasn't worsened," Iraola explained.
"We probably have to be a bit patient until he recovers fully, but it is not like he has to wait a long time to come back."
The Hungary captain has been an important player for Liverpool this season, scoring three goals in eight appearances across all competitions. His return will be a boost as the club manage a demanding schedule.
Liverpool are already without several players through injury, including forward Hugo Ekitike, right-back Conor Bradley and centre-back Giovanni Leoni.
The latest setbacks add to the selection challenges ahead of Tuesday's Champions League meeting with Villarreal at Anfield.
Liverpool have won their opening two matches in the competition, collecting six points, and will look to maintain that perfect record despite their growing injury list.
They are fifth in the Premier League standings with 12 points from seven matches and will hope to build on their win over Brentford as they continue their European campaign.
Liverpool boss Andoni Iraola has revealed that Villarreal counterpart Inigo Perez was his preferred choice to join his coaching staff before a work permit rejection prevented the Spaniard from moving to Bournemouth in 2023.
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