Marco Silva says Andre Gomes will definitely miss Saturday's visit of Manchester City but hopes to see the midfielder return to full training next week.
Gomes has sat out each of Everton's past three games with a rib problem and is yet to rejoin his teammates on the training pitches at USM Finch Farm.
Following the clash with Pep Guardiola's reigning champions, the Blues travel to Burnley on Saturday 5 October.
Silva remains optimistic Gomes could play a part at Turf Moor but won't rush the 26-year-old back to action unnecessarily.
Everton's next fixture would follow the international break when West Ham United visit Goodison on Saturday 19 October.
Speaking at his pre-match press conference on Friday, Silva said: "It is still the same until now - just JP Gbamin [quads] and Andre Gomes will be out.
"Andre is still not working fully with his teammates. Let's hope in the next few days we have some more news about him.
"He's doing some first steps now to integrate into the full sessions with the team. He hasn't yet but it's possible at the beginning of next week he will start, and let's see after how he'll react.
"But if he's not ready for the next match [against Burnley], for sure after the international break he will be ready."
Everton responded to back-to-back Premier League defeats by booking a place in the last 16 of the Carabao Cup with a 2-0 win at Sheffield Wednesday on Tuesday night.
French World Cup winner Djibril Sidibe was handed his second Everton start at Hillsborough and impressed in place of Club skipper Seamus Coleman as the Blues kept a first clean sheet in six games.
Silva believes the Frenchman's display illustrated why he was signed on loan from Monaco ahead of the transfer deadline in August and welcomed the competition the 27-year-old is providing.
"That's why we signed him," said Silva.
"We knew we wanted competition in the side and Djibril will give us that, for sure.
"Unfortunately for us, he didn't do the pre-season and didn't have time to integrate or play in any of our friendly games.
"Of course, in all the moments he's had opportunities to play and get some minutes in his legs, he's done well.
"He's pushing Coleman every time and it will be a good fight between them, I'm 100 per cent sure.
"I believe also we'll see more from Djibril every time he plays and, as he gets to know the Premier League - he's an experienced player but the competition is new for him - we'll see better things."