The party won 28 seats in the 70-member house and formed the government with the outside support of the Congress.
However, after a 49-day stint, chief minister Arvind Kejriwal threw in the towel over the stalling of the Lokpal bill in the assembly.
"We were given a choice of three plots and we even finalised one plot. But we are yet to hear from the ministry" another party member told IANS.
A state party is entitled to getting 500 sq meter plot, he added.
Asked how the party, which claims to be cash-strapped, can afford a high-rent office in a prime location, an AAP member said: "We will ask our supporters to donate the money for the rent."