The audio tape was played on some Telugu news channels but it was not clear who released it.
During the conversation, Naidu purportedly assured the nominated member that he is with him. "Our people briefed me. I am with you don't bother. For everything I am with you. What all they spoke we will honour," Naidu was heard as telling the legislator.
Parakala Prabhakar Advisor (Communications) to the Andhra government strongly denied reports saying that the tapes were fabricated and that the state government will take up the issue seriously.
The reported conversation suggested that the Andhra CM was giving "assurance of all sorts" to the MLA if he votes for TDP nominee in the Telangana Legislative Council election.
Prabhakar further alleged that the Telangana government is trying to malign the image of the Andhra chief minister by resorting to cheap tactics.
"It is not the chief minister's conversation. How come they are available outside? The Telangana government has to answer this. Telangana CM and home minister should give answers," Parakala said.
He said that the Telangana chief minister is trying to mislead the people of Andhra Pradesh by resorting to "cheap tricks".
The anti-corruption bureau of Telangana is in the process of questioning TDP MLA Revanth Reddy and two others who have been arrested in cash-for-vote case.
On May 31, the ACB arrested Reddy for allegedly trying to bribe the nominated MLA Elvis Stephenson to vote for TDP nominee in the Telangana Legislative Council election.
Based on a complaint by Stephenson, ACB officials held Revanth, Sebastian Harry and Uday Simha after they were caught while allegedly handing over Rs 50 lakh to Stephenson.
The audio tape came to light a few hours after ACB questioned Revanth Reddy and others.
Earlier, the Telangana home minister Narasimha Reddy had alleged that Naidu is the key person in the issue.
Photograph: Chandrababu Naidu on Facebook