The England international has been out of action since fracturing his toe during last month's 3-3 draw with Liverpool in the Merseyside derby at Goodison Park.
The player himself recently stated that he was hopeful of coming back into the first team at some point over the festive schedule.
"Leighton is feeling great, but there's still a period to heal," Martinez said in a press conference. "Most likely he's a couple of weeks away."
The Toffees are currently fifth in the Premier League table after 15 games.