The 22-year-old picked up the injury in a pre-season match against Dundee United and Martinez said the club will wait to see if he was available for their home match.
Defender John Stones, who has been strongly linked with a move to champions 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.
Turkish side Fenerbahce has made an offer of 8 million euros ($8.71 million) for Belgian international Mirallas, according to reports in the Turkish media, who have quoted a board member of the club as saying.
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.” – Reuters
Original source: Lukaku fitness worry for Toffees