Griffin had appeared to "like" an Instagram post that ripped Washington, owner Dan Snyder and the front office while lauding Griffin. However, the quarterback later posted his own message to social media, saying the "like" came from an intern who helps with Instagram.
It was the latest twist in the saga between Griffin and the Redskins, after Cousins was named the starting QB earlier Monday.
Some high-ranking Redskins officials and coaches want to part ways with Griffin, who has been sidelined with concussion symptoms, but are meeting resistance from ownership, team and league sources told ESPN on Sunday. The Redskins even have had trade conversations about Griffin with a handful of teams, but they have found no interest, according to sources.
"There have been no discussions about letting him go or doing any of that stuff," Gruden said.
If the Redskins were to release Griffin, it would count $6.7 million against their salary cap. They could trade him, but that could be difficult, in part because of the $16.12 million option Washington picked up for 2016.
However, a source said Griffin could renegotiate the option to help a trade.
If Griffin does stick around, Gruden said he wasn't sure yet whether he would be the No. 2 quarterback or the No. 3, behind Colt McCoy. Griffin, the 2012 offensive rookie of the year, remains in the concussion protocol and might not be cleared until later in the week.
It's not the first time Griffin's social media activity has caused a stir.
In February, an Instagram video of Griffin singing along to Michael Jackson turned into an exchange on his image and how he uses social media. Griffin defended himself in a back-and-forth with a fan that never turned nasty but did amplify views on Griffin's use of social media. There has been a prevailing notion among some fans that Griffin should stop using any social media or performing in any commercials until he starts winning.