Rangers GM Glen Sather has not yet decided if he plans on moving Girardi, who is in the final year of his contract and can become an unrestricted free agent July 1.
If Girardi is moved, the Rangers want a young defenseman and a young forward as part of a package in return.
It's unclear who the Ducks are willing to part with, but it's believed the Rangers would be looking at least for defenseman Sami Vatanen with one of forwards Kyle Palmieri, Patrick Maroon and Rickard Rakell, drafted 30th overall in 2011.
A number of teams will be interested in Girardi if he is officially available for trade, a several, other than the Ducks, have already inquired about his status.
Ducks GM Bob Murray wants to add a rugged, stay-at-home defenseman before the March 5 trade deadline and will look elsewhere if he can't work out a trade for Girardi.