Atrás
The German midfielder has enjoyed a strong start to life at Parkhead following his move from Paderborn in the summer, already a mainstay in the midfield. He has chipped in with four goals as well as being a key cog in the engine room.
Now, a return to his homeland, or England or Italy could be on the table.
Sky Sports in Germany are reporting that clubs in the Bundesliga, Premier League and Serie A have the 22-year-old on their radar.
The report does not mention any names but says "numerous" clubs are in the frame.
Baur recently became a full Germany international after Jurgen Klopp was impressed by his early form at Celtic, although he was called up to the under-21s for this international camp before having to withdraw with injury.
He is contracted in Glasgow's east end until 2030 and his contract does not contain a release clause, putting the club in a strong position.
It is claimed Celtic would be looking for around €15million-20m (£12.5m-16.7m) before agreeing to any deal. Sky Germany add that value could increase before January if his current form continues.