The FA Cup winners are prepared to pay £39m for the Argentinian striker, according to The Telegraph.
Aguero's agent Herman Reguera told Ole: "He wanted the Copa America to end to sit down and talk. During this week everything will be settled.
"In seven days the subject will be closed, but this has nothing to do with money. He wants his career to grow."
Aguero has featured for Argentina in this year's Copa America. His country lost on penalties to Uruguay in the semi-finals, with Carlos Tevez, the player Aguero could potentially replace at City, missing the decisive penalty.