The Frenchman is almost certain to leave Stamford Bridge in January and the Impact could be an option after discussions between player and club went well.
"We did meet with Nicolas Anelka. The discussions were very good. I think there was great potential for a good fit and I think there still is," Marsch told Goal.com.
"I think the organization is open to committed to spending major dollars to bring in good players."
Anelka has been frozen out of the Blues line-up in recent times as manager Andre Villas-Boas opts for other strike options and it is apparent that his career in Southwest London could soon be over.