The 17-year-old has been receiving treatment after he seriously hurt his head in a fall on Wednesday, March 14.
He had spent 13 days in intensive care before being transferred to a high dependency unit.
"Oliver's family has asked the club to once again convey their thanks to everyone for all the messages of support they have received and for continuing to respect their privacy at this time," read a Spurs statement.
"Everybody at the club continues to send their best wishes to Oliver and his family."
Modeste is capable of playing in both defence and midfield.