Schneiderlin has been a peripheral figure at Manchester United over the last two seasons following his move from Southampton in 2015.
The France international has fallen further down the pecking order since the arrival of Jose Mourinho at Old Trafford.
And according to Italian website CalcioMercatoWeb, AC Milan are lining up a loan deal for the midfielder in January.
The report says Milan are keen to have the Frenchman on a temporary basis with the view to making the deal permanent.
It is said officials from the Italian club will bring up a deal for Schneiderlin during their ongoing talks with the United for Memphis Depay.
However, the Red Devils are reportedly looking to offload the former Saints midfielder on a permanent basis.
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Milan are said to want Schneiderlin as a temporary replacement for Riccardo Montolivo who has been ruled out with a long-term knee injury.
But they could face stiff competition from the Premier League, with the Sunday Mirror claiming Crystal Palace are also showing interest in the 26-year-old.
Schneiderlin has made seven appearances in all competitions for United this term but it yet to start a game in the Premier League.
He is under contract at Old Trafford until June 2019.