Momentum built quickly through Saturday as the two clubs moved to finalise personal terms and paperwork, a shift reflected in Hutchinson's absence from Forest's matchday squad for the 2-2 draw at Liverpool earlier that afternoon.
Asked afterwards about Hutchinson's situation and the possibility of further departures before Tuesday's deadline, head coach Oliver Glasner said: "Let's see.
"If we have definitely one, potentially two and probably three signings, it would make sense if we have definitely one, potentially two and probably three players who will leave us."
Hutchinson, 22, will link up with former Manchester United boss Rúben Amorim at San Siro if the move goes through, having already faced his future manager on the pitch earlier this season - he scored against Amorim's United in the Portuguese's first game in charge of the Premier League side, a 1-1 draw with Ipswich Town. Forest signed Hutchinson from Ipswich for a club-record fee of around £37.5m last summer, and he has since made 41 appearances in all competitions, contributing one goal and eight assists.
The winger, who came through the youth ranks at Arsenal and Chelsea before a breakthrough loan spell at Ipswich, has found himself further down the pecking order under Glasner following the Austrian's appointment this summer.
AC Milan, who are searching for attacking reinforcements after confirming Rafael Leão's departure to Galatasaray, are working to arrange a medical for Hutchinson as they push to complete the paperwork before the transfer window closes.
Nottingham Forest are understood to have preferred a permanent sale given the outlay involved in signing Hutchinson only a year ago, but with Milan reluctant to commit to an unconditional obligation to buy up front, a structured loan with performance-based conditions has emerged as the workable compromise for both parties.