The right-back is a doubt for the tournament as he has not featured since March 13 due to a pelvic problem.
England manager Roy Hodgson is planning to send members of the national team's medical staff to Tottenham's training base next week.
"An England physio and doctor will assess Kyle and make a decision," Sherwood said in Friday's press conference. "There is not yet any definitive decision from my side regarding him playing for Tottenham or for Roy. We finish next week, so it will be next week now."
Hodgson will name his 30-man provisional squad on May 12.