According to MailOnline's Dominic King, the Bundesliga duo are both interested in the forward and, with Brewster's scholarship deal set to end in the summer, he could depart Anfield.
The Englishman has been eligible for his first professional contract at Liverpool since he turned 18 at the beginning of last month, but he has yet to commit his future to the Merseyside club.
He may well think that he needs a move elsewhere to get regular game time.
Jurgen Klopp's current front line effectively picks itself, with Roberto Firmino, Mohamed Salah and Sadio Mane all having dazzled consistently in 2017-18.
Danny Ings and Dominic Solanke are the trio's main back-ups, but they have only been afforded a combined 752 minutes of action in the Premier League this season.
The prospect of Brewster becoming a first-team regular at Anfield any time soon seems unlikely.
Per Football365's Daniel Storey, a move to the Bundesliga makes perfect sense:
Daniel Storey @danielstorey85
Brewster is seven days younger than Jadon Sancho (11 Bundesliga games in 17/18). Before summer arrivals, probably ninth in line to play in Liverpool front three: Salah Firmino Mane Ings Oxlade-Chamberlain Lallana Solanke Woodburn Brewster No-brainer. https://t.co/TU5TEl5uEv
He would follow in the footsteps of fellow English youngsters Jadon Sancho and Ademola Lookman, who have both recently swapped the Premier League for Germany. Sancho moved to Borussia Dortmund from Manchester City in the 2017 summer transfer window, while Lookman is at RB Leipzig on loan from Everton until the end of the season.
Brewster is a player of enormous potential.
He starred for England's under-17 side as they won the FIFA U-17 World Cup last summer, picking up the Golden Boot after netting eight goals.
He could be a brilliant addition at either Leipzig or Gladbach, where he would be sure to get more game time than at Liverpool.