The 31-year-old moved to Old Trafford for £14.4m after 13 years at Bayern Munich to link up with former manager Louis van Gaal.
United’s Premier League title win in 2012/13 remains the club’s most recent success and Shaw believes the arrival of Schweinsteiger and Memphis Depay will help their cause.
On the German World Cup winner, Shaw told Sky Sports News HQ: “He’s a massive legend. For someone with that much experience to come into the team will be vital to help us push for some trophies this season.
“He’s one of the most humble guys I’ve come across. He’s not not too loud and he’s quite funny at the same time. It’s nice to have a German around in the dressing room.”
Full-back Shaw has impressed in the build-up to the new season and looks certain to start in the season opener against Tottenham on Saturday in front of his home fans.
Another new arrival Depay, a £31m signing from PSV Eindhoven, is also likely to feature at Old Trafford at the weekend and has also caught the eye of Shaw.
“I’ve got on well with Memphis Depay. He’s a different character,” said Shaw. “It’s good for the changing room and he’s confident about his own ability.
“It’s something new to have but it’s very good to have.”
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