Phillips had made 11 appearances for the German side, who are currently third in the second tier aiming for promotion back to the Bundesliga.
Klopp expects the 22-year-old to be available for the FA Cup third round tie at home to Everton on Sunday week.
“He's our boy, he's on loan at Stuttgart and is doing really well there," said Klopp.
“For people who don't know, Stuttgart pretty much should be, together with Hamburg, the best team in the second division. They are third in the moment, they want to get promoted obviously, and they unfortunately sacked the manager because they are not happy with third place so you see how ambitious they are.
“They are a football-playing side and Nat is doing there really, really well. He played, I think, 11 games.
“Now we have the situation that we have and we thought 'what can we do to help us a little bit?' and we asked Stuttgart if they would be ready to give him back to us for a while and they said 'okay'.
“I don't think we asked Nat, actually, but he looked really happy yesterday (Friday) when he was in the dressing room so it's just a nice story that we can do something like this. I hope that from Everton he will be available."
The manager added: "The two guys who play if Nat is not playing: one is (Marc-Oliver) Kempf, who is a big prospect in Germany, and the other one is Holger Badstuber, a former German international for plenty of years, so he has to fight for his place there.
“But how I said, when he was playing he was really good and hopefully we can see that here as well."