The Toffees boss has virtually ruled out Kone's return before the end of the campaign with Gibson also seemingly likely to struggle to be back in the current season.
It leaves Martinez's squad short on numbers and he will strengthen when the transfer window opens.
"We are going to use the window in January to try to help the team because we lost two players for the long term," said the Spaniard.
"Arouna and Darron are two very important players for us so we will try to see if we can identify one or two players that can help the group.
"We have been working hard to identify who can help the group and that is what we are looking for in January."
Martinez admits his initial fears Kone would not recover from an operation to repair damaged cartilage in time to play a part in the remainder of the season have materialised.
"Arouna started the first part of his recovery and it is going to be long-term, as expected," he added.
"I don't think we are going to see Arouna this season.
"If we can get him back for the final two months he will have done really well.
"There was a big chunk of cartilage that had to be repaired in his knee.
"In the same manner we are hoping we can see Darron Gibson before the season ends but clearly it is a long-term injury as well."