Ronny Deila stressed his desire to keep Fraser Forster at Celtic following the 4-0 victory over KR Reykjavik.
Executive vice-chairman Ed Woodward insists Manchester United are ready and willing to break the British transfer record.
The Germany Under-21 international has been with the club since joining the youth team in 2002 and is pleased to agree fresh terms, which have not been disclosed.
"Here at SC, the club's management and the coaching staff fits and I can develop everything here, it's nice that I get confidence here and now can give something back," he told the club's official website.
Baumann, 23, recently made his 100th Bundesliga appearance for Christian Streich's men.
Freiburg sporting director Jochen Saier added: "We are delighted that even Oliver Baumann has decided to extend his deal with the club.
"Oli has in, the last three Bundesliga seasons, become an important support of our team and one of the best goalkeepers."