On Thursday, the board had been set to discuss hiring an interim director while it probes the harassment allegations against executive director Carl Greene.
But PHA chairman John Street says the board wasn't able to get all the information it needed and tabled any discussions until Sept. 23.
The board put Greene on indefinite leave last month while it looks into how the agency settled multiple sexual harassment claims against him.
Greene filed suit against PHA earlier this week, claiming breach of contract and violation of his due process rights.
A federal grand jury and the U.S. Housing and Urban Development agency are also investigating.
