Media outlets report project manager Mike Barham says the company plans to begin moving a 100-foot-tall drilling rig onto the site on June 29.
Barham says once the rig is in place, the drilling is expected to last about 30 days. The project's first phase involves drilling a 13,000-foot-deep vertical well.
The announcement comes as the Louisiana Supreme Court considers whether to hear an appeal from St. Tammany Parish and a citizens group against the project.
Some residents and officials say the drilling could pollute the air, the ground, and the aquifer that supplies St. Tammany with drinking water.
Helis officials have said they'll drill safely and safeguard the environment.