Milan manager Massimiliano Allegri is on the look out for an additional left-back to provide competition to Taye Taiwo in the starting line-up.
And according to Sportmediaset, the Rossonerri have pin-pointed the Brazilian defender as the ideal player to fit into their backline.
The 30-year-old has appeared to be a surplus to requirements at the Nou Camp, where the likes of Eric Abidal and Adriano are preferred at the left-back department,
Therefore, Maxwell would be interested in rejuvenating his career elsewhere, and Milan could be the perfect place for him to do so.
Milan are hopeful of signing Maxwell on a one-year loan deal and Barcelona appear to be ready to say farewell to the former Ajax ace.
Maxwell was signed from Inter Milan in 2009.