Rafa Benitez has confirmed Lucas Digne, Seamus Coleman and Alex Iwobi have returned to full training - but it is too soon to make a decision over anyone’s availability for Sunday’s meeting with West Ham United.
The strike duo of Dominic Calvert-Lewin and Richarlison, along with Everton captain Coleman, missed the four matches immediately prior to October’s Premier League shutdown.
Manager Benitez was additionally without Andre Gomes and Iwobi for the 1-1 draw at Manchester United two weeks ago.
Left-back Digne, meanwhile, returned early from France duty nursing a minor hamstring complaint – and fellow defender Yerry Mina is set to play for Colombia against Ecuador on Thursday night.
For Ben Godfrey and Salomon Rondon, two players whose seasons started late, the past fortnight represented an extended chance for physical conditioning.
“The international break is an opportunity to bring back players,” said Benitez.
“Alex Iwobi was training and [so were] Digne and Coleman – that is good news for us – they have started training with the team.
“The others are improving and we will see in the week how they are.
“Lucas had an issue and for two or three days was under treatment but he has started training.
“Fingers crossed [for Yerry Mina], hopefully everything will be fine in the last game, then we will see [if he is ready for West Ham].
“Every day when they [Godfrey and Rondon] train, they are improving.
“Salomon is scoring goals in the training sessions and Ben is defending really well.
“This time will benefit everyone but especially these players who were not fully fit.”
Anthony Gordon has been banging on the First-Team door since Benitez’s appointment in pre-season and it swung open for the Academy graduate when he began the meeting with United at Old Trafford.
Gordon's first league start of the campaign followed a 90-minute outing in the Carabao Cup game at QPR 11 days previously.
“The way he is training and the way he behaves in the training sessions [got him in the team],” said Benitez.
“He is keen to learn and always ready to improve parts of his game.
“He knew he had to be more consistent and work harder with and without the ball and he is doing that.
“We are talking about a young player but he has the potential to be a great player if he continues working the same way.
“Anthony has all the attributes to be really good but if we talk too much about him it will be bad for him.
“He has to stay humble and keep working as hard as he is now.
“He knows, because we had this conversation, that he needed someone shaking him and saying, ‘Come on, wake up, you have the potential, but still you have done nothing’.
“He understands this is the only way to be as good as he can.
“The way he manages this season will be crucial for him to be a very good player in the future.”
Gordon has featured in seven of nine matchday squads this term.
But asked if the 20-year-old is now viewed as a First-Team squad fixture, Benitez put the ball in Gordon’s court.
“That is a question for him more than me,” said Benitez.
“Why? Because I could say 'Yes', then in the next few weeks he does nothing and we are considering his future.
“The main thing now is he mentally continues being as strong as he showed us, that he can be here, because he has the potential to be really good.”
Everton’s encounter with West Ham is followed by games against Watford, Wolverhampton Wanderers and Tottenham Hotspur before another international break in early-mid November.
“If we can keep the same intensity [as opening months] I will be really pleased," added Benitez.
“But we have to improve a little bit on the ball… we are so dangerous on the counter-attack and up front, sometimes it is better for us to wait and play on the counter-attack.
"The final-third decisions are much better but still you want even better in other areas.
"I am really pleased with the attitude of the players and I am sure they will continue improving on and off the ball."