The characters Pravarakhya and Varudhini are from a Hindu Purana named Markandeya Purana. This story occurs when the sage Markandeya, the narrator of the text, gives out the incidents that lead to the birth of the Swarochisha Manu, the one whom the text Manu Charitra is based upon.
Allasani used that incident and enlarged the work by adding descriptions of Himalayas, the background of Pravarakhya, conversation between characters, how Pravarakhya and Varudhini felt after they met and parted, and other modifications.
Markandeya Purana Chapter 58 contains the details and the story of Pravarakhya and Varudhini. One can read the complete story as narrated by Markandeya.
Here is a summary:
There was a learned youth named Pravarakhya living in a town called Arunaspada on the banks of the River Yamuna. He observed regular rituals and served guests who visited him. This gave him extreme happiness. A Siddha (learned man with magic powers and knowledge of medicinal herbs) visited Arunaspada and he was served by Pravarakhya. Pravarakhya was enthusiastic about the Siddha and asked how he was able to travel to a lot of places at such a young age. The siddha revealed that had a magical medicinal herb which helps him to travel to any place at his will. He just applied it to his feet and then closed eyes. In the next moment, the destination would be reached. Pravara had been keen to visit places for a long time and he requested that herb. Siddha was pleased with the devotion and service offered by Pravarkhya and gifted him that tree root and went on his way.
Pravarakhya desired to visit the Himalayas and closed his eyes. In the next moment, he was there. While he was engaged in admiring the natural beauty of the Himalayas, the exotic root which was applied to his feet melted away due to the water present in the Himalayan mountains. That left him stuck at that place. He laments his decision to visit a place so far away from his home. He feels sad for his wife waiting for him. In search of his way home, Pravarakhya finds a damsel named Varudhini and asks her why she was wandering in such a place alone. She replies that she is the daughter of Menaka, an apsara (a celestial nymph). She asks if it was his habit to talk to women in that way. But Pravarakhya gets defensive and then answers that he was genuinely interested in finding his way home. But she doesn't believe him and she admits that she has fallen in love with him and she wants him to marry and embrace her. If rejected, she will give up her life. He denies her, saying he is already married and is engaged in regular rituals. It is mandatory to marry a single woman to indulge in his daily rituals.
He prays to Fire God (whom he worshipped regularly through rituals) that it is getting time for evening ritual and he should perform it as a duty. Fire God answers the prayers and takes him back to his home by carrying him on his shoulders. However, Varudhini still loved him. Meanwhile a Gandharva youth, whose offers to Varudhini have been rejected by her over several years now, assumes the form of Maya Pravarakhya and shows up while Varudhini is saying in desperation that if Pravara would not change his mind, she may as well end her life! Maya Pravarakhya (disguised Pravarakhya) replies that the srutis (Vedas, the sacred texts of Hinduism) declare one must not skip rituals and at the same time, it also says that one should not be the reason for a woman's suicide. So, he accepts her offer on the one condition that she should not open her eyes while they were united. She readily agreed to that condition. The condition was set because Gandharvas (a race of celestial beings) restore their original form while they are performing union with women. The couple had a happy time for some time but she realized that he was a Gandharva. She cursed him to be born as a miserable human being. As a result of this union, Varudhini bore a child named Swarochi with radiant features and strong mental faculties. This Swarochi is the father of Swarochisha Manu, the second Manu who is the main character in Manu Charitra.