Currently a free agent, Modric had already made clear he wanted to wait until after the World Cup before deciding whether he still had the motivation to continue with Milan, particularly following last season's disappointing campaign and Massimiliano Allegri's departure.
Retirement at 41 or a romantic return to Dinamo Zagreb had both been considered among his options, but a further year in Serie A now appears the most likely outcome.
AC Milan are also weighing up the future of Yunus Musah, with Leeds United having made contact over a possible move for the American midfielder in recent days after interest from several clubs across Europe. Musah returned to Milan this summer following a loan spell at Atalanta, who opted against making the move permanent after he struggled to find consistent form there last season.
No final decision has yet been made on his future, with Amorim set to assess him closely during July's pre-season training before giving the club clearer guidance on whether he should stay or be allowed to leave.
Milan, meanwhile, look set to miss out on a player identified as one of Amorim's leading defensive targets, with Antonio Silva no longer expected to join the club. The Portuguese centre-back, a product of Benfica's academy, has repeatedly turned down contract renewal offers from the Portuguese club, whose 2027 deal with Silva leaves the door open for other suitors.
Milan had considered Silva one of two priority targets in defence alongside Goncalo Inacio, but Sky Sport report the 23-year-old is now closing in on a move to Bournemouth, with sporting director Tiago Pinto, a long-standing admirer of the player, pushing to complete the deal.
Silva is coming off a strong campaign in Portugal, making 25 league appearances for Benfica and contributing one goal and one assist, in addition to six Champions League outings before the club's exit under Jose Mourinho. His imminent move to the Premier League would represent a blow for Milan's recruitment plans in defence, leaving Amorim to reassess his options at centre-back as the summer window progresses.