The injuries also prevented the Villa pair from representing their countries at the weekend, with Heskey missing England's defeat by Brazil and Collins sitting out Wales' win over Scotland.
However, O'Neill is optimistic that Heskey and Collins will be fit for the weekend's trip to Turf Moor after making progress in their recovery.
"The medical staff are quite happy with the progress they are making," said O'Neill in the Birmingham Mail.
"They still have quite a number of days before we are back in action."
O'Neill will also have Habib Beye and Stiliyan Petrov back from suspension for the game against Burnley, but he has yet to decide whether to make changes to a winning team.
He added: "We will see how the lads come through training.
"I'm not looking too far ahead, especially as we have Richard Dunne involved for the Republic of Ireland before we have him back."