The Spurs legend has not played since early November after being injured in the home defeat by Aston Villa.
Gazza needed surgery on a hernia problem after he hobbled off in that Sky Sports live game.
However, Toffees’ boss Walter Smith is wary of bringing him back too soon.
Smith said: "He's obviously very keen to be involved at the weekend but his progress will have to be monitored."
Along with Gazza, Richard Gough and Abel Xavier are making significant progress after injury and they too could feature against us.
Smith added: "We have to be careful that we don't cause any further problems to any of the injured players that have been out for a reasonable spell. So, we will take our time and make sure that is the right time for them to be playing again."
Back at Spurs, Ben Thatcher and Luke Young may be ready to feature after playing 90 minutes for the reserves on Tuesday.
Paul Gascoigne could return to action after a two-month absence for our Premiership clash Goodison Park on Saturday.