According to the Albany Times-Union, the two are friendly, speak often and Cuomo has "pledged his full support" to Eldridge, a Cuomo adviser said.
Democrats consider Gibson vulnerable, as he represents a district that President Obama won by 6 percentage points last cycle.
And Eldridge, who is married to Facebook co-founder Chris Hughes, would have the funds, and the support from the Democratic establishment, to launch a strong challenge.
The Cuomo adviser told the Times-Union that the governor “will be available in any way the campaign decides they can use him," and has spoken highly of Eldridge to his associates.
Democrats currently hold 201 seats in the House, 17 short of a majority, and Gibson's district is one of a few dozen they're targeting in hopes of taking back control of the lower chamber.