Reports in the New York Times and Fox News say Mr Obama is planning to extend protection from deportation to some parents of legal US residents.
The overall plan is estimated to affect as many as five million undocumented immigrants living in the US.
Republicans in Congress say such action would be beyond Mr Obama’s authority.
“We’re going to fight the president tooth and nail if he continues down this path,” House Speaker John Boehner told reporters.
Mitch McConnell, the incoming Senate majority leader, urged the president to “work with us to try to find a way to improve our immigration system”.
I find Obama’s decision to go through with immigration reform (affecting up to 5 million immigrants) without involving Congress to be outrageous. I am not an Obama supporter obviously, but I would be alarmed if any President I supported did this to the opposition - it would force me to reconsider my support of him. Not only is he thumbing his nose at the Republicans, he is thumbing his nose at every single US citizen who disagrees with his policies, or who even just wants a congressional debate on this issue.