But the proposal did not get off the ground after Mr Rubio argued that the US should settle for nothing less than regime change.
The second proposal, presented in September, would also have seen Mr Maduro replaced by Ms Rodríguez, who would head a transitional government, while the deposed leader would seek exile in Qatar or Turkey.
Ultimately, this was also rejected by the US, which believed that the regime’s criminal structures would simply be repackaged under new leadership. “The ‘Cartel Lite’ was not a viable option,” one source said.
Reports on meetings between Ms Rodríguez’s team and the Americans went quiet towards the end of the year.
Intermediaries, meanwhile, assured the administration that she would promote American energy investments, making her an easy choice to run a transition at least.
“I’ve been watching her career for a long time, so I have some sense of who she is and what she’s about,” one senior US official told The New York Times.
“I’m not claiming that she’s the permanent solution to the country’s problems, but she’s certainly someone we think we can work at a much more professional level than we were able to do with him,” the official added, referring to Mr Maduro.
However, US officials cautioned that their relationship with the interim government will be based on whether Ms Rodríguez operates by their rules and that they could take further military action if she fails to respect American interests.