Shaqiri, 25, helped Stoke end United's 100% start to the season by holding Jose Mourinho's side to a 2-2 draw at the bet365 stadium on 9 September.
The Switzerland international, who spent three seasons playing for Basel, said if the Red Devils had one area of weakness it was in defence.
"That's what our goals have shown. If you play quickly and bravely, their defenders will have problems," Shaqiri was reported as saying by the Daily Mirror.
"At the back, Manchester are vulnerable. We are physical and tactical. We did not hide.
"You have to play bravely. It does not matter if you lose. Man United have so much class in their attack."
Shaqiri conceded that it would not be easy for Basel to get a result at Old Trafford, but urged his former side to be brave and play attacking football.
"It will be extremely difficult for Basel. Especially at Old Trafford , where Manchester is much more dominant than away from home," the former Bayern Munich winger said.
"Old Trafford is one of the best stadiums in the world. [Basel] have to be brave, risk something. Just defending will not be enough.
"I admire [United manager Jose Mourinho]. He does not care what people think about him. He knows how to set up a team perfectly."
Shaqiri also commented on Paul Pogba's strong start to the season and claimed that the France international had a tendency to hog possession in midfield.
"It's hard to separate him from the ball," he said. "But he sometimes tends to keep the ball too long. Also, physically, he is very strong."
United are top of the Premier League table by virtue of their superior goal difference compared to second-placed Manchester City.