Favre, who took over Gladbach midway through last season and helped them stay up thanks to a relegation playoff win, has a contract until 2013. He has turned the former German champions into title contenders with their best first half of a season in 35 years.
"I am in constant dialogue with those responsible and I am delighted with the recognition of my work," Favre said after club bosses this week expressed their wish to renew their working relationship and discuss it in the coming weeks.
The 23-year-old, who has been at Stuttgart since childhood, joined sports directors Fredi Bobic and Jochen Schneider who also penned new deals to 2016.
"In a difficult year for him, Sven was superb and developed as a keeper," said Stuttgart coach Bruno Labbadia. "He embodies the VfB."
Stuttgart play at Schalke 04 on Saturday.
Hamburg SV could resume their Bundesliga recovery against champions Borussia Dortmund on Sunday without forward Mladen Petric and offensive midfielder Ivo Ilicevic, coach Thorsten Fink told reporters.
Both are nursing calf injuries and missed training on Thursday.
"They are both injured but it's not certain yet that they won't be able to make it," said Fink.
Hamburg, after being anchored in last place earlier in the season, are now in 13th place with former Bayern Munich player Fink yet to taste defeat in his eight league games at the helm.