Need advice for switching company

I have got an offer and they are expecting me to join in a month in worst case. I am currently billable in my project and billable swon was allocated until Feb end

Should I resign first or get release from the project and resign. I have not told to my manager about the new job offer. I am thinking if I tell them about new job offer they would ask me to do notice for 3 months rather i am asking them to release me

Note: there is no dependency on me, they kept in the project for some new project work since i got released from current team

Please advice