The Togo international was granted permission to return to Africa earlier this month to deal with a "private matter", and has not featured for the club since a 2-1 home defeat to Stoke City on November 9.
Adebayor has since returned to training, and could feature when Spurs host Burnley in the Premier League on Saturday.
"He's available," said head coach Mauricio Pochettino. "After, we will see if I pick him or not.
"I'm happy with Ade and how he's been training. Maybe he's not 100 per cent yet, but he's not far away.
"He's getting better. He needs training, he needs to improve, especially his physical condition, but he's getting better."
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