The `Anger Management` star set up his account on the micro-blogging site in March 2011 and gained more than a million followers in 48 hours but sources close to the actor have claimed he "feels like he`s not getting anything out of the social network" and wants to shut down his page, which now has almost eight million followers.
It is not clear when - or if - Charlie will shut down his page but gossip website TMZ.com say it could be a matter of days or even hours.
Meanwhile, Charlie has revealed he wants to be an `American Idol` judge.
The actor said he would consider joining the judging panel of the singing show if the money was good enough and programme bosses donated part of his salary to charity, after producer Nigel Lythgoe said he wanted him to get involved.
He said: "If the numbers move the needle AND `Idol` matches 20 per cent of my weekly salary for Autism Speaks, JDRF, and the Boys and Girls Club ... then the hell with it. As we say, pour the smoke. (sic)"
However the actor would only agree to a deal if FX, which airs `Anger Management`, were happy with him appearing on Fox.
Steven Tyler recently quit the panel and Jennifer Lopez is heavily rumoured to be considering leaving the series.
Charlie, 46, is due to appear on the 1,000th episode of WWE `Raw` next Monday (16.07.12) as the wrestling company`s Celebrity Social Media Ambassador.