Solanke starred and scored in victory at United on Saturday.
Hargreaves told PLP: "I would take him to Manchester United, definitely. At Chelsea he was the prized academy player. He went to Liverpool - who had that brilliant front three. The front trio of that generation. He would never break in there.
"But I think he learned and was guided by (Roberto) Firmino, (Sadio) Mane and (Mohamed) Salah. We saw that with Wilf (Zaha) when he went to Manchester United. He wasn't ready. He was too young.
"I think that Solanke will now have another big transfer.
"Regardless of whether it's Man United or not. But to get such a big and technically good guy, who is smart enough, can run and press. He will get another chance at the top level, I'm sure."
