The 21-year-old had been earning rave reviews for his performances across 17 Scottish Premiership appearances that returned two goals.
On Beck, the Liverpool boss said: “We were always pretty positive about Owen, but then he had two really difficult loan spells [at Famalicao and Bolton last season].
“It was a surprise that it didn’t work out because of what we thought about Owen, but that’s how it is with young boys.
“When you send them away from home, plenty of things can happen.
“Things always have to fit well – it must be the right manager, must be the right team, if they have another left-back there who is experienced.
“There are so many things which can make a loan spell not really happen.
“But at Dundee everything was fine and he made big steps.
“Now the situation here is clear – we lost two of our left-backs so it makes a sense to bring back a boy we like who is available to us.”
Later in his press conference, Klopp confirmed the club’s plans for both Phillips and Williams.