Tony Hibbert has resumed training with the rest of the Everton squad.
The right-back hasn't featured since last month's pre-season friendly at Blackburn after picking up a knock but has now stepped up his return.
Darron Gibson is also on the road to recovery with his fitness being closely monitored by boss Roberto Martinez.
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The Spaniard told evertontv: "Darron Gibson is still recovering from his niggle. It is one of those situations where we have to be very, very careful. You are risking losing him for a long period.
"He's not far away and I do expect him to be involved before the international break but it's too early to tell if he will be back for Saturday."
Everton stalwart Hibbert resumed training with his teammates earlier this week.
Martinez continued: "We are keeping a close eye on Tony Hibbert now he has joined the group, which is really positive news for us.
"He joined the group yesterday [Monday] and had no reaction, so we are going to step him up a little bit more. He's not far away from being available for selection."
Magaye Gueye is also back training with the squad but Martinez reiterated that neither he, Gibson nor Hibbert were certain to make the weekend's visit of West Brom.
He explained: "It is too early to tell if they will be in the squad on Saturday, the next 48 hours are going to be very important but we will find out on Thursday or Friday."
Another in the treatment room, Antolin Alcaraz is likewise nearing a return and could be back in time to face Cardiff City at the end of this month.
"I expect Antolin Alcaraz to be fit over the coming weeks so it's all positive," said Martinez. "I would say the Cardiff game is most realistic, or the international break. He has been working really hard and the medical department have done a great job with him."