The 22-year-old was absent for Liverpool's 5-1 win over Porto in the Champions League and omitted from England's squad for World Cup qualifiers against Andorra and Hungary.
Klopp expects Alexander-Arnold to return after the international break along with midfielder Thiago Alcantara, who is recovering from a calf injury.
"They are doing well but they won't have enough time for being back against City," said the German coach.
"But we have a good team so we still have solutions and we have to use them and yeah, after the international break the boys will be back I think."
Liverpool, who drew 3-3 with Brentford in the league last weekend, top the table with 14 points. City are a point behind in second.