The former Bristol City boss led the Glovers into the Championship for the first time with victory over Brentford at Wembley earlier this month before opening talks to stay at Huish Park.
With his contract due to expire this summer Yeovil have been quick to meet with Johnson and chief executive Martyn Starnes revealed that those discussions have gone smoothly so far.
"Discussions are continuing in a positive and constructive manner," he told the Western Morning News. "Everything so far has been positive."
Meanwhile work on the Huish Park pitch will start within the next seven days.