According to Football Italia, AC Milan are hoping to sign the 34-year-old on a permanent basis having impressed since joining the club on loan in the January transfer window.
Sergio Conceicao’s side will ask parent club Man City for a discount, however, with qualification for Champions League football come the end of the season looking unlikely.
Walker has been key for Milan, making nine appearances across all competitions as they continue to struggle both domestically and on the continent.
AC Milan currently sit down in ninth, six points behind fourth-placed Bologna ahead of their trip to high-flying Napoli once the international break is over.
The Serie A club will seek to sell Emerson Royal to help earn funds after becoming increasingly frustrated with the Brazilian’s performances.