Sky Bet were forced to slash their odds on Baumgart becoming the next manager at Parkhead to 18/1, placing him within the top ten candidates for the role.
Neil Lennon remains the favourite to take over on a permanent basis at 1/2 but the German offers an intriguing alternative for Chief Executive Peter Lawwell and the Celtic board.
The 47-year-old took Paderborn to promotion last season and they currently sit third in Bundesliga 2 behind Hamburg and Cologne, with only a handful of games remaining.
The former FC Magdeburg and Berliner AK boss is understood to be highly rated, but has no experience of the Scottish game having spent his entire career in Germany.
Other names in the frame for the manager’s hot seat include Kilmarnock boss Steve Clarke (10/1), Belgium manager Roberto Martinez (5/1) and former Chelsea manager Andre Villas-Boas (8/1).