The 47-year-old currently manages Bundesliga 2 side SC Paderborn.
The Hoops appointed Neil Lennon as their interim manager, following Brendan Rodgers’ departure midway through the season.
Despite Lennon’s impressive run, a swarm of managers were linked with the full-time manager job and now the German has joined the list.
Baumgart commenced his managerial career with FC Magdeburg, the club which he had earlier played with.
He had a decent spell with the Bundesliga 2 side, eventually winning the FSA-Pokal in 2019.
The former VFL Wolfsburg striker later moved to Berliner AK 07.
Upon joining Paderborn in 2017, Baumgart made an immediate impact, helping his side to earn a promotion in Germany’s Tier 2.
He is also having a great time this season, as Paderborn are currently third in the Bundesliga 2 table.
Odds are high for Lennon
The former Hibernian manager hasn’t faced a defeat since taking charge, securing six wins.
Notably, the Old Firm derby win and the qualification for the Scottish Cup final has enhanced his chances of becoming the permanent manager for the Celts.
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The Bhoys are on the verge of clinching their eighth straight League title, while their chances of winning a domestic treble also remain high.