The hostage crisis involving the 32-year-old IAS officer entered the tenth day on Monday.
The chief minister told reporters in Raipur that the fourth round of talks between the government-appointed mediators and those on the Maoists' side was underway, and he was hoping for an early resolution, with both sides finding "agreement" on certain points.
The interlocutors from the Maoists side had met the ultras two days ago, and they conveyed the Maoists' stand to the government, Singh said.
Government mediators Nirmala Buch and S K Mishra briefed the sub-committee of Chhattisgarh cabinet, which is dealing with the crisis on the Maoists' demands, he said. Soon a solution would emerge and the sub-committee would take the "final decision", he added.
Menon was abducted by the Maoists on April 21. The ultras have demanded release of 17 of their jailed leaders, among other things, for his release.
Maoists-side mediators, B D Sharma and Professor G Hargopal, met the ultras in the Tadmetla forests, and briefed them about the talks. The collector was said to be in a "good health".