Kirovski has impressed management with how he has been guiding Forza Milan, the club's B team.
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Forza Milan now compete in Serie D after relegation last season and are in the mix for the promotion playoffs.
Kirovski's current deal expires at the end of the season and carries a 12 month extension, which Milan intend to trigger, says Tuttosport.
The American recently said: "We also want to win every game, because I think it's important for Milan to put pressure on our players because when they arrive at San Siro they'll play under pressure.
"But our number one goal is to to help them grow."
