The renowned German beer festival is held annually in Munich and attracts visitors from around the world.
Schweinsteiger, signed from Bayern Munich last month, has proposed a team trip for United - but is unsure whether it will get the go-ahead from manager Louis van Gaal.
"I once said to Wayne [Rooney, United's captain], if we have the time, I want to invite the team to Oktoberfest," Schweinsteiger told Sky Deutschland.
"I do not know if we have that much time, and if it has the coach's approval."
Schweinsteiger made his competitive United debut as a second-half substitute in Saturday's 1-0 victory over Tottenham in their Premier League opener.
