Osman suffered a cut on his left eye in the early stages of Everton's 3-0 win over Arsenal last Sunday and required stitches to close the wound.
The 32-year-old has made good progress since suffering the injury in the ninth minute, and manager Roberto Martinez is confident Osman will be ready for their trip to the Stadium of Light on Saturday.
"Obviously the first 24 hours were important, he is recovering really well," he told Everton's official website.
"We'll assess him and take it from there, but it is too early to say how quickly he will join the group.
"Knowing Leon, he will be ready and I will be very surprised if he doesn't make the squad for Saturday."
Osman has been a regular for Martinez this season with 24 starts in the Premier League, and five appearances in the domestic cup competitions.
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