Mr Rai said the party was "yet to take a final call" on its nominees.
The party approached former RBI governor Raghuram Rajan to be its candidate, but he is believed to have declined the offer.
An AAP leader, requesting anonymity, said last week that the party was looking for an economist, an eminent jurist and a known name in the field of social service to represent the party in the Rajya Sabha.
This was also being done to put to end to the rancour within the party over the Rajya Sabha nominations.
The AAP has 66 members in the 70-member Delhi Assembly and its victory on all three seats looks certain.
The tenure of the three incumbent Rajya Sabha members from Delhi ends on January 28, 2018.
Talking to reporters at an informal briefing on Friday, Mr Rai said the party was exploring all possibilities.
Many AAP leaders are reportedly vying for the Rajya Sabha nomination.
Kumar Vishwas is considered to be a strong contender for a Rajya Sabha berth, but looking at his rocky relationship with the leadership at the moment, his nomination looks unlikely.
Asked whether anyone has made their ambition clear for the Rajya Sabha seats, Mr Rai, in a dig at Kumar Vishwas, said, "There aren't many insecure people in the party."