The move would see Kroesche take on the role of Head of Football at the Serie A club, ending a five-year spell in which he helped transform Frankfurt into a regular fixture in European competition.
Moretto's report has since been corroborated by fellow transfer journalist Fabrizio Romano, suggesting the deal is now in its final stages.
According to reports in Germany, Eintracht Frankfurt's sporting director Timmo Hardung is also expected to follow Kroesche to Milan, taking up a role alongside his colleague at the San Siro.
Kroesche joined Eintracht Frankfurt from RB Leipzig and has overseen a period of significant improvement for the club, including a third-place Bundesliga finish and Europa League quarter-final run during his tenure.
His contract with Frankfurt runs until 2028 and includes an exit clause, though that clause is not active again until early 2027.
That means Milan will need to negotiate directly with Frankfurt over a compensation fee to secure his early release, according to German outlet SPOX.
The move comes amid wholesale change at Milan this summer. The club's previous leadership group, including manager Massimiliano Allegri, sporting director Igli Tare, chief executive Giorgio Furlani and technical director Geoffrey Moncada, were all dismissed after Milan missed out on Champions League qualification.
Ruben Amorim is close to being confirmed as Milan's new head coach, with reports from Corriere della Sera suggesting the former Sporting Lisbon and Manchester United manager has agreed a two-year deal with an option for a third season, worth around €3.5 million per year plus bonuses.
Kroesche's arrival would complete a significant overhaul of AC Milan's football operations, with the club looking to rebuild a structure capable of returning the Rossoneri to the Champions League.
For Frankfurt, losing both Kroesche and Hardung in the same window would represent a major blow to the football department that has underpinned the club's recent progress.
The financial details of any compensation package for Kroesche remain to be resolved between the two clubs, with reports suggesting Frankfurt are likely to demand a significant fee given his importance to their recent success.
Whatever the final figure, Milan appear determined to move quickly, with the appointments of Amorim and Kroesche together signalling the scale of the rebuild Gerry Cardinale and RedBird have planned for the club this summer.