Gase took up his current post during the off-season, when McCoy left to become the new head coach of the San Diego Chargers.
The 35-year-old told the team's website: "It will be [an] interesting deal. It will odd seeing him on the other sideline. [This is the] first time in four years that we haven't worked together.
"I know it doesn't seem like a long time to other people, but when you're together every day for four straight years it's a different feeling.
"I think that's the most important thing that I've learned from him is just that constant preparation, the way he called the game he did a really good job of getting the play calling quickly and letting the quarterback do his job."
Gase has previously been the Broncos' wide receivers and quarterbacks coach.