The 54-year-old leader had taken over as the Congress's Delhi unit chief four years ago, after the party lost the 2015 assembly elections.
Later, Maken took to Twitter to announce his resignation.
"After the 2015 Delhi assembly elections, as its Delhi unit president, I received a lot of love and support from Congress workers, the media covering the party and our leader Rahul Gandhiji. It was not easy in these difficult times. Thank you all," he tweeted.
The party had in September last year denied reports of Maken's resignation and had said that he had gone abroad for a medical checkup.
Maken's resignation assumes significance amid speculations of a possible alliance between the Congress and the AAP in Delhi for 2019. He was strongly opposed to any truck with the AAP in the national capital.
The sources said former chief minister Sheila Dikshit could replace Maken as the Congress's Delhi unit president. She has maintained that the party high command's decision on alliance will be accepted by her.
The AAP and the Congress have not yet denied the speculations.
Congress leaders Yoganand Shastri, Rajkumar Chauhan, Haroon Yusuf and Chatar Singh could also be considered for the post of the party's Delhi unit chief, the sources said.