Honda “fulfilled a childhood dream” when he signed for the Rossoneri on a free transfer from CSKA Moscow in 2013.
But despite making a positive impression initially, the 29-year-old has fallen steadily out of favour following the departure of coach Filippo Inzaghi at the end of last season.
Under new coach Sinisa Mihajlovic, Honda has made eight appearances in 11 games but a lack of regular starts has left the Japanese frustrated and disillusioned.
A report on the Sky Football Night programme said Honda, whose contract expires in June 2017, has reached agreement with Milan’s CEO Adriano Galliani to remain at the club until the end of the season.
It also said he would refute any offers from interested Premiership clubs during the January transfer window to remain with Milan and help them reach their prime objective of a top three finish and a return to the Champions League.
Milan, who have failed to qualify for Europe’s premier club event over the past two seasons, have enjoyed a purple patch of late and won their third league game in succession for the first time this season with a surprise 3-1 win at Lazio last weekend.
It moved Mihajlovic’s men up to sixth place at just five points behind leaders Fiorentina ahead of Saturday’s visit of Atalanta. – Agence France-Presse