Liverpool midfielder Szoboszlai to miss key cup clashes through injury
Hungary international Szoboszlai was substituted after 64 minutes in Liverpool's 4-2 Premier League win over Newcastle United on Monday.
"It is an injury... muscle, hamstring. I don't know, we have to see. Dom is very positive. He doesn't have a lot of pain, but we have to wait a little bit," Klopp told reporters ahead of Sunday's game at the Emirates Stadium.
"No chance obviously for Sunday, not for Wednesday, and then we will see after that. Hopefully he might be back, but we don't know.
"Besides that, nothing else really happened. The rest were yesterday available and fully fit, so let's hope that stays the same and we will have to make a choice."
Liverpool will also be without Mohamed Salah as the attacker links up with the Egypt squad for the Africa Cup of Nations, while they will also miss combative midfielder Wataru Endo who will join up with Japan at the Asian Cup.
"I said if I wish them good luck it would be a lie. Hopefully, they are out in the group stages but it's not likely possible," Klopp said.
"Good luck and hopefully they can come back healthy. I am pretty positive we will find a way (to replace them) but we have to show that. Other players can play on the wing but not like Mo, it's not possible...
"Do we want to play without Mo? No. But we will find a way. Of course, we play Arsenal and we can lose with Mo Salah, but at the moment we have a chance to win the game, so we think about that."
Liverpool's match against Arsenal takes place three days before the meeting with Fulham.
Asked if the short turnaround between the games would make it necessary to rotate his squad, Klopp said: "I am not sure if Arsenal is a game to rotate. I am not sure we have the opportunity to do that.
"We can line up a good team and I am sure that is what we will do. We have a few days between games, so that is long enough and there is no need for rotation.
"We want to win these games, we want to go to the League Cup final but also the next round of the FA Cup, but it's probably the most tricky draw you can get."