The Daily Express says City boss Pep Guardiola has held talks with the former Barcelona captain about a short-term deal this month.
Guardiola wanted Busquets as cover for Rodri as he recovers from his ACL surgery.
But the veteran has rejected the prospect as he prepares for his second season in MLS.
Guardiola confirmed: “No - because he is so happy in Miami. The weather there is so delightful! I spoke to Sergio, not for that issue, but quite often. We have the same agent, so I’ve been in touch for many years.”
On City's search for Rodri cover, the Catalan also said: “There are players that can do it (Rodri’s role) - but clubs don’t sell or they are so expensive.
“So we cannot do it but of course we thought about that because Kova and Gundo are helping us, but they are not proper, proper holding midfielders. We know that, so they are making an incredible effort and we are grateful for that.
“Many times over a tough period I know perfectly the players who stepped up to try and solve our problems we have with commitment and effort. That is why I am so grateful to a few of them.”