Barnes thinks bringing Thiago to Anfield may affect the balance Jurgen Klopp currently has in his team.
“With the midfield being very workmanlike, they are a lot of points better off than everybody else," Barnes told BBC Sport.
He added: “The reason you can have two full-backs attacking at the same time and three strikers is because they have three hard-working midfielders to protect that situation.
“If you get another creative midfielder and you want your full-backs and front three to attack, then maybe you are going to concede more goals."
Barnes continued: “Manchester City have got how many creative players in their midfield? But Liverpool finished 20-odd points ahead of them. Maybe Manchester City should say: 'Let's get more hard-working players in midfield so we can catch Liverpool.'"