The BBI secretariat says they have collected over 1.5 million signatures.
The team on Monday said it expects to hit three million signatures by Thursday next week.
The exercise will end on Thursday.
The 1.5 million signatures include those obtained through the online app.
One million signatures of registered voters are required to back the draft constitutional amendment Bill.
ODM Chief Raila Odinga and ANC boss Musalia Mudavadi urged people to come forward and sign because its the future of the country.