The Germans collected a 2-1 win at home in the first leg of the Champions League last-16 tie.
Sancho is reportedly a summer target for United and Chelsea, and Hargreaves believes it would be a wise signing.
Hargreaves told BT Sport: "That performance from Sancho was like Neymar in his prime. Off the cuff. He was unplayable.
"Get your cheque books out. Somebody go and sign that kid because he is special."
Former Spurs midfielder Jermaine Jenas added: "He showed maturity beyond his years. He's a spearhead for them with what he brings, his lack of respect for the opposition.
"You always felt like he was going to do something tonight. That tells me he thinks he is the best player on the pitch."