The Swiss side travel to Old Trafford tomorrow (7.45pm) for their Champions League clash.
And with United in great form so far this season, it proves a daunting task.
But Shaqiri’s Stoke became the first team to take points off United this season on Saturday.
The Potters drew 2-2 with the Red Devils in their Premier League encounter ahead of United’s return to European action.
And while Shaqiri hailed the likes of Jose Mourinho and United’s qualities, he feels they have weaknesses too.
“You have to play bravely,” Shaqiri told Swiss newspaper Blick.
“It does not matter if you lose. Man United have so much class in their attack.
“If they do it’s with their defence. That’s what [Stoke’s] goals have shown.
“If you play quickly and bravely, their defenders will have problems. At the back, Manchester [United] are vulnerable.”
Paul Pogba and David De Gea could both start for United tomorrow.
And on the star pair’s flaws, Shaqiri added: “It’s hard to separate [Pogba] from the ball. But he sometimes tends to keep the ball too long. Also, physically, he is very strong.
“[De Gea is] an absolute world class goalkeeper. Extremely strong on the line, good with the ball at his feet. Very quiet – maybe even too quiet.
“It will be extremely difficult for Basel. Especially at Old Trafford, where Manchester is much more dominant than away from home.
“Old Trafford is one of the best stadiums in the world. [Basel] have to be brave, risk something. Just defending will not be enough.”
Shaqiri has confirmed he will be in attendance at Old Trafford to watch Basel take on Manchester United.
