Liverpool are third in the Premier League with 10 points from four games in one of their strongest starts in history, thrashing Aston Villa on September 3rd in their last game before the break.
"We would've loved to have carried on after the Aston Villa game, which was a really good game," Klopp told reporters on Friday.
Alexander-Arnold, who injured his hamstring against Villa, has resumed running and will likely start work "soon."
"They barely heal in two weeks; this one didn't," Klopp said.
The German coach was concerned about the short turnaround from recent international games.
"I think 30-odd hours ago, Alexis Mac Allister played in Bolivia, landed yesterday morning at four o'clock. So, let's see where we can pick up," Klopp said.
Liverpool bolstered their squad in the close season, adding Argentina's Mac Allister, Hungary's Dominik Szoboszlai and Japan international Wataru Endo after losing midfield stalwarts Jordan Henderson and Fabinho to Saudi Arabia.
"The quality of the players, I'm really, really happy, the potential we have is really good," Klopp said.
"And I love working with them, they are open. It's nice for a manager as well, to know they didn't hear it already 500 times before, that some messages are new.
"(This is) year one of a new team, we want to become a new team and not a replica of the other team and that is what we're working on."
Klopp bristled however when asked about Mohamed Salah's future. Reports said Liverpool rejected a 150 million-pound bid for their talisman by South Arabian club Al Ittihad in the recent transfer window. Klopp was asked if the Egyptian forward may be sold in January.
"A week after the transfer window, you ask about January? Are you kidding?" Klopp said.
"You can't wait! I'm not worried, we will see what happens."
Liverpool have won 12 of their last 13 Premier League games against Wolves, who are 15th with three points.
The Merseyside club have only earned 10 points or more from their first four games eight times in their 108 previous seasons in the top flight.
