Leon Osman and Arouna Kone could return for Everton against Newcastle, while Steven Pienaar is not yet ruled out.
All three of those players missed the Capital One Cup defeat to Fulham in midweek.
But Roberto Martinez said at his press conference ahead of the Premier League game on Monday night that Osman and Kone were progressing well and could be available.
The Blues boss also said that Pienaar could 'never be ruled out' because of his natural fitness, adding that he will monitor the South African ahead of the game against the Magpies.
It means the only player definitely out is Antolin Alcaraz who has suffered a setback with his groin problem and is three to four weeks away from a return.
Martinez said: "Arouna Kone and Leon Osman have progressed very well so it wouldn't be a surprise if they were available.
"The two we are still a little bit concerned with are Antolin Alcaraz and Steven Pienaar. With Stevie, you can never rule him out because he is such a fit boy and maybe over the next two sessions he could become available for the squad.
"Antolin is definitely out, but in general the news is positive in players recovering and becoming available."
Darron Gibson could continue in midfield after making a successful return from injury on Tuesday, while it would be Romelu Lukaku's home debut if the on loan Belgian is selected to play.
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