Kane underwent surgery on a hamstring injury on Saturday after suffering a ruptured tendon at Southampton on New Year’s Day and Spurs have said they expect him to be back in training some time in April.
Mourinho has been asked repeatably when exactly the England captain might return, but has not been able to be more specific.
He was again questioned ahead of Spurs‘ FA Cup replay with Middlesbrough on Tuesday and his throwaway answer suggested there could be some doubt over Kane’s participation at the European Championships this summer.
“News on Harry we don’t have and if you ask me every time we come here the answer will be the same,” Mourinho said.
“We expect him to be out until, I don’t know, mid-April, end of April, May, next season I don’t know.
“I have no updates to give on Harry.”
Kane tweeted from his hospital bed that his operation had been a success and that he was keen to get on with his recovery.
The striker has a history of recovering quickly from injuries, but Mourinho’s comments will concern England boss Gareth Southgate ahead of a summer tournament where his side play their three group games at Wembley.
Kane was the leading scorer in Euro 2020 qualifying with 12 goals.
The Three Lions play their first game of the tournament against Croatia on June 14.