The former Bristol City boss has taken Yeovil to their highest ever finish and they will do battle with Sheffield United over the next seven days for a place at the League One play-off final at Wembley.
Johnson's current deal expires in the summer but Starnes is hopeful he will sign an extension.
"We had talks in the week and the club is amenable to what Gary is looking for," Starnes told BBC Somerset.
"Talks have been going on between Gary and the owners. We've got everything on the table.
"If a one-year rolling contract is something Gary would be interested in then we'd talk seriously about that. If he wants a fixed-term then we'll look at that as well.
"That dialogue is continuing but there are a lot of distractions at the moment."
That first distraction comes at Bramall Lane on Friday night as Yeovil, who won 2-0 on that ground earlier this season, take on Sheffield United in the first leg of their play-off semi final.