The Bavarian giants dominated both domestically and in Europe last season, wrapping the league title up with six games to spare before going on to capture DFB-Pokal and Champions League honours.
However, Favre said that his team do not fear going to the Allianz Arena on the first day of the season, suggesting that it may be better to face them sooner rather than later.
"Maybe it's even an advantage for us [to play them on the opening weekend]," coach Lucien Favre told Der Westen newspaper.
"We have to play against them sooner or later. There are 34 matches in the Bundesliga and not one easy weekend. We have no fear of Bayern."
Monchengladbach finished eighth last season.