Heitinga is expected to return to training this week after overcoming a groin injury, while Kone is still struggling with an ankle injury sustained earlier this month.
Manager Roberto Martinez told the club's official website: "Johnny Heitinga is recovering really, really well. He has progressed as we expected over the weekend but is possibly ahead of the time we set for him.
"Arouna Kone had a really nasty incident against Hull City late in the game and that has swollen his knee. So we are going to assess him over the next two or three days and see the extent of the problem.
"I think the Spurs game may be too early for both of them but it is still early in the week. Everyone else is back to where they should be."
The Toffees are currently sixth in the league table.