The meeting in the evening lasted for about 15 minutes after which Naidu refused to speak to the media outside Singh's residence at Ashoka Road in Delhi.
The chief minister-designate of Andhra Pradesh had on Tuesday said his party would join BJP-led NDA government at the Centre.
"We are joining the government. TDP was part of four non-Congress governments at the Centre. We would be part of NDA as well," he had stated but did not say how many cabinet berths his party would get in the central government to be headed by Narendra Modi.
Leaders of NDA allies like TDP, Akali Dal and LJP, are also likely to be included in the Council of Ministers.
TDP, which faced the elections in alliance with BJP, won 16 Lok Sabha seats in Andhra Pradesh. The party is also forming the government in residual Andhra Pradesh.