The 17-year-old striker, who was an unused substitute at the Etihad Stadium on Sunday where Liverpool drew 1-1 with Manchester City, has played for the Wales’ Under-19s and was propelled into the senior squad by Coleman following only seven first-team appearances at club level.
Asked if he had spoken to Coleman about Woodburn’s call, Klopp said: “Actually, I was surprised about this. I don’t know exactly how it’s normal here. This should not be a criticism, but usually when you call up a player, a 17-year-old player, I thought it would be possible to call me.
“I’m not sure if he knows him well. He didn’t play in the team so far for Coleman I think. But no call.”
Woodburn, who became the club’s youngest goalscorer in November, has joined up with Coleman’s squad to begin preparations for Friday’s World Cup qualifier against the Republic of Ireland in Dublin but Klopp would have preferred the Nottingham-born player to stay at Liverpool to continue his development away from the spotlight.
“If he stopped learning now, that would make no sense at 17,” said Klopp. “I’m not in doubt about this. We didn’t hide him, we used him all the time. He’s a fixed part of our training. He can deal with the nomination for Wales 100%.
“It’s a little bit like my situation. As long as you give me the time, as long as we give him the time, everything will be good.
“He has to learn, he has to develop, he has to improve, all of this. That’s why I said there are now two managers responsible for him. Until now, it was only my job.”
Of Woodburn’s call-up, Coleman said: “If I thought it was too early for him I wouldn’t have called him up, because this game is massive for us. I am thinking about what is the best squad to get together to meet this next challenge. And Ben has done enough.
“As far as I see he is a Welsh international. He hasn’t played for England or Scotland. He’s played for Wales since a young boy, so it’s just that natural progression.”
The Liverpool captain, Jordan Henderson, meanwhile, has travelled with the squad for warm weather training in Tenerife but Daniel Sturridge has been left behind.
Klopp has taken all of his senior players not on international duty – such as James Milner, Dejan Lovren, Joël Matip, Loris Karius, Alberto Moreno and Lucas Leiva – to the Canary Islands for the week.
Henderson has been sidelined with a foot problem since the victory over Tottenham in February but Klopp expects him to be fit to return for the Merseyside derby at Anfield on 1 April.
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