Barca are open to letting Junior leave the club and are looking at possible replacements should he depart this month, although the lack of a president at Camp Nou is complicating any potential January transfer business.
Milan are keen to bring in backup for Theo Hernandez, with the versatile Diogo Dalot their only alternative at left-back, to strengthen their squad as they fight for a first league title in Italy since 2011.
Sources have told ESPN the Serie A leaders have enquired about taking Junior on loan, although Barca, in need of money, would rather let him leave on a permanent deal.
West Ham would be willing to sign Junior, who cost Barca around €20 million from Real Betis in 2019, but cannot guarantee first-team football, either, with Aaron Cresswell performing well at left-back for David Moyes' side.
Junior, 24, wants to leave having found regular football hard to come by but Barca are reluctant to let him go without first lining up a replacement.
The Blaugrana have made moves to find a new left-back but they are not in a position to sign players this month following the delay to the club's presidential election.
A new president will not be elected until March 7 and the three candidates for the presidency -- Joan Laporta, Victor Font and Toni Freixa -- all voted against handing acting president Carles Tusquets the power to make signings this month.
Manchester City defender Eric Garcia was a candidate to re-join the Catalan club in January but all three Laporta, Font and Freixa all agreed it would be irresponsible to spend money the club doesn't have now when Garcia is available for free in the summer when his contract expires.