The former is expected to be out for three weeks with a thigh strain, while McGivern is struggling with a hamstring problem.
Hibs were already without James McPake - who is recovering from an operation on his back - and the Leith side are short of options in defence ahead of the visit of Celtic on Sunday. Butcher is now desperate to add to his squad.
"We're going to have to work even harder to get one or two in," said the Hibs manager, who has been linked with a move for former Inverness striker Adam Rooney. "We've made progress but we'll certainly try and conclude that this week."