Hammers boss Avram Grant has identified Barton as the ideal replacement for former Newcastle midfielder Scott Parker, who is expected to leave Upton Park in the summer.
Barton is due to enter the final year of his current deal in June, and Alan Pardew had hoped to tie him down to an extended agreement at the turn of the year.
Newcastle owner Mike Ashley has made it known EVERY player has his price, and Jose Enrique (who is in an identical position to Barton) is another player ready to fly the Magpies roost.