The Everton midfielder has already apologised after cameras caught him butting the Stoke defender during a 1-1 draw at the Britannia Stadium.
And in two separate incidents Fellaini appeared to aim an elbow at Shawcross and push him in the face in retaliation for being held around the chest at a corner.
In theory, the Belgian could be banned for each incident if referee Mark Halsey missed all three and retrospectively rules each was worthy of a red card.
The Football Association is reviewing footage of the game and, under its rules, any charges must be issued by 6pm on Tuesday.
Fellaini is also likely to be fined by Everton after manager David Moyes publicly condemned his player.
Moyes said at the weekend: "We will accept whatever punishment is given out for it.
"I have told him in the dressing room that it is not acceptable and whatever gets handed out he and us deserve it."
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