Swansea manager Garry Monk hopes to get at least two new faces in before the end of the transfer window.
Sky Sports understands Chelsea starlet Islam Feruz is in line for a move to Russia with FC Krylia Sovetov.
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."