The 19-year-old has made just 13 appearances in all competitions for the German champions this season, six of those coming as a starter.
Denmark international Hojbjerg appears unlikely to gain more playing time in a crowded Bayern midfield that includes the likes of Xabi Alonso, Bastian Schweinsteiger and Mario Gotze.
And his representative Soren Lerby has revealed that Hojbjerg is set to make the move to the SGL Arena for the remainder of the campaign.
Lerby told Kicker: "The six months will be good for him. He will play matches."
Augsburg sit sixth in the Bundesliga at the halfway point of the season, having taken 27 points from 17 matches.
If the move is completed Hojbjerg could make his debut on February 1 when Augsburg host fellow European hopefuls Hoffenheim.
