Chris Coleman wanted to bring the 18-year-old forward to Sunderland on loan for the rest of the season in a bid to aid their Championship relegation battle.
The Black Cats gaffer made a request to Liverpool but, according to The Sun on Sunday, Klopp insisted he is staying put.
Coleman knows Woodburn well, having worked with him at international level.
The Liverpool ace became Wales’ second-youngest ever goalscorer when he netted on his debut against Austria in September.
Woodburn enjoyed a breakthrough campaign last season, making nine appearances for the Reds.
But he has found first-team opportunities hard to come by this term, featuring just once in the EFL Cup.
Liverpool handed Woodburn a long-term contract in October.
“It’s an unbelievable feeling to sign a new contract with Liverpool,” he said.