Healy struck Cole's ankle while the Leicester tighthead lay prone once an Ireland maul had collapsed, in an incident that received widespread condemnation.
The 25-year-old will appear before an independent Six Nations disciplinary committee in London on Wednesday.
The recommended suspension for a low end stamping offence is two weeks, the mid range five weeks and top end nine weeks, up to a maximum of one year.
England took exception to the incident and a large brawl erupted, although referee Jerome Garces failed to spot what ignited the flare-up and Healy evaded punishment on the pitch.
It is hard to envisage Healy, a leading contender for selection by the Lions in Australia this summer, escaping censure on Wednesday given that television replays clearly show the stamp.
A two-week ban would ruled him out of Ireland's next Six Nations assignment against Scotland on February 24, while a more extensive suspension would also threaten his involvement against France and Italy.