The 36-year-old left the San Siro at the end of last season and has since been linked with a move to a number of clubs as well as a switch to the MLS.
However, Ambrosini's agent Moreno Roggi admits that his client is likely to make the switch to Florence and stay in Italy rather than join West Ham.
"We are close to defining something," Moreno Roggi told Radio Blu.
"He will enter a new group and be ready to take whatever role is asked of him.
"Florence is a really beautiful town and the club has a big project."
Ambrosini spent 18 years with Milan.