Officials from the Home, Public Works and General Administration departments discussed urgent preventive measures to break the streak.
One of these measures under considerations is fixing a safety net across the first floor, similar to the one used at under-construction high-rises, said a PWD official.
"We will discuss some immediate solutions tomorrow at the Mantralaya and see if they can be implemented immediately," he said.
"A man from Marathwada had tried to jump off from the parapet of one of the top floors a few months ago. The home department had (then) carried out a survey of the building and came up with some recommendations," he said.
"A detailed plan can be executed in coming days step by step, as it takes time and funding. But some of the measures should be implemented at the earliest," the official added.
On Wednesday, a 32-year-old jobless man attempted suicide outside the building, the police said.
With the two incidents, preceded by similar attempts coming in quick succession, the opposition was quick to attack the BJP-led government, dubbing Mantralaya as the new "suicide point".