Acquah clash with Toure in the final of the 2015 Africa Cup of Nations in Equatorial Guinea two months ago where Ivory Coast triumphed on 9-8 on penalties.
After the final, Acquah claims Touré told him: “you will be my heir at Manchester City.”
“We went into a challenge, he dived and simulated injury. I wagged my finger at him. Yaya Touré was always my idol,” 23-year-old Acquah told Secolo XIX newspaper.
“Once the game was over, he called me and we talked. He said that I played well and one day I’d be his heir at Manchester City.
“For now, my City is Samp. I am still in contact with Touré, though.”
Acquah eventually missed a penalty in the decisive shoot-out and admits it was traumatic.
“Every time I take a penalty in training, it comes back into my mind. I watched the whole Final back on TV and cried.”
Acquah is only on loan at Samp until the end of the season, having arrived from Hoffenheim on transfer deadline day last month.