Barkley has not played for his country since the friendly against Australia prior to Euro 2016, but was handed a recall last week by boss Gareth Southgate for the Nations League matches against Croatia and Spain.
"It's a new experience for me because Klopp has a different style of work from the way I'm used to - but this is something I will learn".
"If somebody would have told me after eight match days you have 20 points, I would say with that fixture list, "I'll buy it, let's start with the ninth match day", said Klopp.
"It has been nine wins in a row in all competitions, but I'm not sure the opposition in those games has been so good that they can get over-confident about their run and their title chances".
He said: "I'm over the moon to be back, I feel like it's been a long time coming but I feel like I have worked hard over the last couple of years and that it's fully deserved that I am back here".
Man City and Liverpool are regarded by many as the two title favourites - but the London clubs certainly look like they're in with a shout.
Klopp said players need a proper break to be fresher, pointing to the case of Liverpool midfielder Jordan Henderson who played for England at the World Cup in Russian Federation.
"I think it is not about these games, it is all about the other games, the hard games which we have against mid-table and lower teams", he said, as quoted by The Mirror.
US Senators trigger probe into journalist disappearance
While Riyadh claimed he had left the consulate after his visit, Turkish police said Khashoggi did not emerge from the building. News of Saudi Arabia orchestrating the assassination of Khashoggi has put further pressure on its ally the USA to take action.
With a two-week break for worldwide matches, we asked Soccer Saturday pundit Matt Le Tissier for his verdict on the start of the 2018/19 campaign. "But after eight games I still think it's very early to think about Chelsea challenging [Man City or Liverpool]".
On a personal level, I'm really enjoying my time with Chelsea.
"They're unbeaten in the league so I think it's been great".
It's all helped me mature as a person and a player too. We have added a lot of youth to the squad, we are all developing from a young age, developing into big players.
'Against Portugal I nearly had to play as right-back.
"In that situation they are much better than us".
"To show I can produce the goods on game day", he said.