Record signing Lukaku pulled out of the Belgium squad due to a hamstring injury, while a stomach strain prevented midfielder Gibson from featuring for Republic of Ireland.
Fears that Kone was facing another long spell on the sidelines were this week allayed when the striker underwent a scan and Everton boss Martinez hopes all three could take on Ronald Koeman's side at Goodison Park.
He told the club's official website: "Romelu had his scan with the Belgian setup and he's going to be receiving treatment for the next few days, and we'll see how that evolves.
"It's a bit of a hamstring strain due to the amount of games that we've played and the amount of fatigue we've accumulated in those games.
"We're quite positive because of the way Rom usually reacts to these types of treatments and how fit he is as an individual.
"It's too early to say how long he's going to be out or if he's going to miss any games but he's concentrating on getting back fit to train with the group.
"With Darron, he had a little bit of a stomach strain. He made sure that he finished the game (against QPR last weekend) but he felt it in the last 10-15 minutes. After the game, when his body cooled, he then felt a real difficulty walking and trying to exercise on it.
"He's been receiving treatment and obviously he met with the Irish party, and now we're going to assess him and see how long it will be before he can join the group again.
"In both cases, I don't think they are major injuries but they are injuries that need to be well looked after and we'll see if both players are available or not for the Southampton game."
When asked about Kone's fitness, the Spaniard said: "We were delighted with the results of the scan, which showed first and foremost that Arouna's ankle and knee are really strong,
"In the last two days his joints have practically been back to normal, so we're very confident he could be fully fit for the game against Southampton, although it will be important to see him working with the group and see how he adapts throughout next week."
