Right-back Seamus Coleman has missed Everton's last three matches with a hamstring injury, but was reportedly close to a return in Saturday's 1-1 Premier League draw at Liverpool.
Fellow defender Sylvain Distin has not played since the 3-0 League Cup defeat at Swansea, while midfielder Steven Pienaar has been absent after picking up a groin injury in the 2-2 draw with Arsenal at the end of August.
Manager Roberto Martinez, who admitted some of his players were suffering with a virus ahead of the Merseyside derby, is hopeful that the trio will be fit.
"We are going to assess them individually," said Martinez.
"Everyone is progressing well and in a good position to be fully fit very soon.
"There were a couple of players that were a little bit affected by viruses and [felt] a little bit ill.
"They got through the [Liverpool] game really well and now we will assess them to make sure that they are fully fit for Thursday.
"That's the only thing I am looking at - to make sure that everyone who is travelling to Russia is fully fit and can cope with a demanding trip and a difficult game."
Martinez will definitely be without midfielder Kevin Mirallas for the Group H clash in Russia.
The 26-year-old came off during Saturday's Merseyside derby due to a hamstring injury, with the club fearful that the Belgium international faces a lengthy spell on the sidelines.
Everton are awaiting the results of a scan on the injury, but Martinez revealed on Tuesday that the "signs are not great".
The Premier League side opened their Europa League group campaign with an impressive 4-1 home win over Wolfsburg.
However, Thursday's game represents something of a trip into the unknown to face Krasnodar, who drew 1-1 at Lille in their opening game.
The Russian outfit beat Spanish side Real Sociedad 3-0 on home turf to secure a 3-1 aggregate win that secured their place in the group stage.
One Everton player who does have some insight into Thursday's opponents is winger Aiden McGeady, who faced them on six occasions during a three-and-a-half season spell with Spartak Moscow.
"It will be a tough game," the Scot told Everton TV.
"They have some money behind them and have bought some players and climbed the league.
"It is their first time in Europe so I would expect a good crowd and these places are never easy to go to."