Beck, Phillips and Williams are three of five players that have returned to Liverpool from loan spells during the winter window, the others being Fabio Carvalho from RB Leipzig and James Balagizi from Wigan Athletic.
There's also the possibility that the Reds recall young Scottish right-back Calvin Ramsay from his loan spell with Preston North End.
Phillips spent the first half of the season with Celtic and was always due to return to Anfield in January, but struggled for game time in Scotland. As did centre-back Williams, who didn't register a single senior appearance during his time at Aberdeen.
The two defenders, who famously formed a successful partnership amid Liverpool's defensive injury crisis during the 2020/21 season, don't seemingly have too much of a future at Anfield, with Klopp discussing their futures prior to the Reds' FA Cup clash with Arsenal on Sunday.
"With Nat we have to see, we have to see," said the Liverpool boss. "We have to consider our own situation and stuff like this. He will definitely be with us until the end of the month and then we will have talks and see our situation, that’s how it is.
"We really think highly of both [Phillips and Williams], to be honest, because of the things the boys did when they were here.
"Nat, it didn’t work out 100 per cent at Celtic, a little bit injuries but then if a team like Celtic is in a positive moment and you are in the team you stay in the team, if [they are] not in a positive moment and you are in the team then you might go out, so that says nothing about the quality.
"So, Nat will train with us and then we will see how that develops.
"With Rhys it is slightly different, he will be first with the U21s. I will have to talk with him about why his loan spell didn’t work out, that was obviously different and the boy I know I would expect to play in Scotland, 100 per cent, from the first to the last second if it is not Celtic or Rangers where it is always slightly different, and he didn’t.
"I will have to talk to him about that and I didn’t do that yet, but it will happen, definitely, and then we will see what’s the outcome of that conversation."
"It was good," Klopp said of Beck's loan spell in Scotland. "So, we always saw and were pretty positive about Owen but then he had two really difficult loan spells, which was a surprise that it didn’t work out because of what we thought about Owen, but that’s how it is, especially with young boys when you send them away from home and stuff like this.
"Plenty of things can happen there and it always needs to fit really well – it must be the right manager, must be the right team, if you have another left-back there and he has experience… there are so many things [that] can make a loan spell not really happening.
"That was probably for him the case and now in Dundee it was fine and he made big steps, and now the situation here is clear: we lose two of our left-backs so we think it makes sense if a boy we like is available for us, we bring him back. That’s all."
Beck may well earn a start for the Reds against Arsenal in the FA Cup third round this weekend, while Phillips and Williams could take residence on the bench.