Defender John Stones, who has been strongly linked with a move to Chelsea, and Kevin Mirallas are expected to shake off their injuries while new signing Gerard Deulofeu also has not been ruled out, the manager added.
"Gerard Deulofeu could be available for the weekend. I also expect Kevin Mirallas and John Stones to be fit," Martinez told reporters on Thursday.
Martinez admitted England international Stones has been affected by the interest shown by reigning Premier League champions Chelsea.
"Clearly John is one of the outstanding young talents that we have in the squad and you are going to get that sort of interest from the outside," Martinez said.
"John is an Everton player and there is nothing else to comment on that."
Martinez might also have to deal with the interest shown by Turkish side Fenerbahce for Belgian international Mirallas and according to reports in the Turkish media, an offer of 8 million euros ($8.71 million) has been tabled.
Former Wigan Athletic manager Martinez wants to bring in three more players to strengthen his squad.
"Pre-season has been a positive period and we've given youngsters an opportunity. We need to bring more three players into the squad," Martinez said.
"We will never bring a player in for the sake of it and to fill a position. We are looking for the right characteristics."
(Reporting by Shravanth V in Bengaluru; editing by Sudipto Ganguly)
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