The Manchester rockers parted ways with Zac Starkey earlier this week and have reportedly requested that Sharrock replace him.
A source told The Mirror: "Oasis and Robbie have an ongoing feud. This move is sure to infuriate Robbie.
"Everyone thinks Chris has had enough of sitting on the picket line and not playing music. Oasis aren't striking against anyone so at least he'll be getting a bit of action now!"
Starkey, who is the son of Ringo Starr, allegedly left the group after falling out with Noel Gallagher during the recording of their seventh studio album.
Previous Oasis drummers have included Tony McCarroll, Alan White and Terence Kirkbride.