The Japan international has made one substitute appearance this season, totalling just 11 minutes on the pitch.
The 30-year-old has been linked with a move to Southampton and Claude Puel is fan of his talents.
However, according to Calciomercato, Honda looks set to move to the MLS during the January transfer window instead.
Los Angeles Galaxy, New York City FC and New York Red Bulls are all interested in the playmaker and have offered him the chance to head to America.
All three clubs are reportedly open to taking Honda on loan or signing him permanently.