The France international, who has been linked with an exit this summer, has not been well in the past few days so he has not travelled to the States for the summer tour.
His absence is likely to raise further questions over his future, though, after a disappointing first campaign at the club following his big-money move from Newcastle 12 months ago.
The midfielder made just eight Premier League starts last term and is a top transfer target for Marseille, who are keen to take him back to France.
Meanwhile, Erik Lamela, who has a hip injury, Danny Rose (knee) and Heung-min Son (arm) have all also stayed behind to continue their recoveries.
Spurs play Paris Saint-Germain, Roma and Manchester City in the International Champions Cup tournament over the next week and a half in the US as the build-up to the new campaign continues.