The Uruguayan is currently in England with his country for the Olympic Games and his representative has indicated that he could stay there amid interest from the champions
Goal.com revealed in May that City was leading the chase for the Uruguay international and his representative, Pablo Betancur, indicated he is in talks with an English top-flight club.
Speaking to calciomercato.com about Ramirez’s future, Betancur said: "I think it's always been more likely that Gaston says goodbye to Italy. So much so that now I'm in London to talk with a Premier League club.
"I think Ramirez will leave. He is one of the best players and so there are many offers and, again, I think it's unlikely he will remain in Italy."
The winger scored eight goals for Bologna in Serie A last season to help the club to a ninth-placed finish and had attracted interest from the likes of Inter and Wolfsburg but Betancur admits Bologna’s asking price is too high for them.
"Inter like the player but we are very far off from what Bologna are asking for him - nearly 25 million pounds," he said.
"The Wolfsburg interest? They were the first to move on Ramirez, but some of the figures are impossible for them too.”