The Japan international was linked with a move to the Serie A club throughout the close-season, and has reportedly signed a pre-contract agreement at San Siro, but has now revealed he has other offers available to him.
Both Liverpool and Arsenal have both been linked with the 27-year-old in the past and may also be in the running to sign the attacking midfielder.
Honda - speaking after Japan's 3-1 friendly win over Ghana - announced that his three-year stay in Russia will end but placed question marks over where he will move to.
"Milan? They are an option, but not the only option," he said. "When the time comes, I will make a decision.;
"I have now decided I will leave my club at the natural expiry of the contract."
Honda has made 109 appearances during his spell in the Russian capital, scoring 26 goals and winning the league title last season.
