"The idea may take three months to develop," he told reporters on the sidelines of the Independence Day function here.
The chief minister cited an incident which took place earlier this week when a man, his wife and daughter all committed suicide. Police said the family was depressed following the death of their only son a week earlier.
"Such a case would have been known to people living nearby and preventive action could have been taken to avoid the tragedy... These cases would be identified by the cell, which can have representatives of the public and NGOs on them," Parrikar said.
He said the idea was not fully crystallised yet but the government was working on it.
The chief minister said that despite the government's outreach, there were still people and families who were out of the support system network and who needed assistance.
"Earlier there was a support system... village people used to come and help, but now there is none," Parrikar said, adding that such a support network was necessary.