McCoy started last Sunday against the Indianapolis Colts after Robert Griffin III was benched. McCoy threw for 392 yards and three touchdowns with zero interceptions in a 49-27 loss that dropped Washington's record to 3-9.
"You don’t want to have competition at that position all the time," Gruden said. "You’d like to have a guy you can say, 'Hey, this is our quarterback, fellas. Let’s build our team around him!' And then you have the competition between No. 2 and 3."
"We’ll see what happens these last four games. Then as a staff we’ll have to talk about the future of the position — whether we’re going to build around Colt, whether we’re going to have a competition between Colt and Robert and Kirk [Cousins]."
On Friday, Jason Reid of the Post reported Gruden could be "one and done" with Washington after this season. According to Reid, a conflict between Gruden and Griffin could force the team to part ways with the head coach, who is in the first year of a five-year contract.
Reports emerged last week that Gruden is "done" with Griffin and would prefer the team to make a "clean break" with the quarterback this offseason.
ESPN's Adam Schefter, however, has reported there is a "real chance" Griffin could be reinstated as Washington's starter at some point this season.
Griffin has struggled in his third NFL season, completing 69.7 percent of his passes for 869 yards, two touchdowns and three interceptions while going 1-4 as a starter.
- Molly Geary and Mike Fiammetta