Mani was optimistic that the GST Bill "will go through", though he did not share the details.
During the meeting, sources said, various aspects of the legislation were discussed.
The 21-member Select Committee is headed by BJP MP Bhupender Yadav.
Mani, the Finance Minister of Kerala, had yesterday called on Union Finance Minister Arun Jaitley.
"Some states are asking for compensation, some states are asking for review of additional tax. Those things have to be decided," he had told reporters after meeting Jaitley.
The Centre proposes to roll out GST from April 2016. The Lok Sabha has already cleared the Bill.
States are pressing the Centre for compensating them fully for the loss of revenue in the first five years of the introduction.
The Centre has agreed to compensate states fully in the first three years and partially in fourth and fifth year.
The issue of compensation, besides other matters, was raised at a recent meeting of the Empowered Committee.