MacKenzie, 66, was the editor of The Sun in 1989 when the newspaper made a number of false claims about fans involved in the Hillsborough disaster.
"It beggars belief they would even consider the man," Hillsborough Family Support Group chair Margaret Aspinall is quoted as saying by the Liverpool Daily Post.
"National newspapers should know the history of Hillsborough and the people involved.
"I thought they would have more sense - let's hope they've learnt lessons from this."
The 24th anniversary of the Hillsborough disaster will be marked on April 15.