With speculation swirling around the Stuttgart midfielder, the former Germany international admits turning down a club of United's stature would not be easy.
"If I look at Manchester United purely from a sporting perspective right now, I would probably say yes," Strunz told Football Presse.
"But of course it is a huge name. Manchester United is a super name."
However, Strunz also pointed to the uncertainty that has surrounded the English giants since the departure of Sir Alex Ferguson.
"Since Ferguson left, we have had the feeling that things are not really moving in the right direction."
Even so, he knows what it would mean to reject such a famous club.
"To say no to a club like that is not easy."
But Strunz believes Stiller is thinking long term.
"I think he is smart enough. He knows he is in a good place in Stuttgart. He became a national team player there. He still needs more. He wants to keep developing."
In Strunz's view, patience will pay off.
"He will continue to develop. And then the time will be right for him to take that next step."
It is a decision he admires.
"Very wise, very clever. It says a lot about him."
Strunz also highlighted what makes Stiller such an attractive prospect.
"I think he has outstanding game intelligence."
"He has certain qualities that are very, very important in that number six role in midfield."
With praise also coming from German legend Lothar Matthaus, Strunz can see why the hype is growing.
"I can absolutely understand what Lothar is saying. Absolutely."
Manchester United may be calling.
But according to Strunz, Stiller's smartest move right now might just be staying exactly where he is.