Spurs are just one point above the bottom three, without a win in their past 11 league games, while boss Igor Tudor is under intense scrutiny after just four matches in charge.
In a message sent to fans, the London club announced the period to renew season tickets would run until June 7th, after the end of the season.
The club said it recognised the "seriousness of the current league position" and wanted fans to have "full clarity on next season before renewing".
"Everyone at the club remains absolutely steadfast in our collective commitment to improve our Premier League position and finish the current season as strongly as possible," it added.
Former England defender Gary Neville, now a television pundit, has branded Tudor's brief tenure a "car crash" that needs to be brought to an end.
The Croatian's position was weakened significantly by Tuesday's 5-2 defeat against Atletico Madrid in the first leg of their last-16 tie in the Champions League.
Tudor selected reserve goalkeeper Antonin Kinsky only to substitute him in the 17th minute after calamitous errors.
Speaking on The Overlap's Stick to Football podcast, Neville said the treatment of Kinsky was "brutal".
"I thought the whole thing of the last few weeks and then that, the whole thing is just a car crash, a shambles," he said.
Tudor was only appointed last month following the sacking of Thomas Frank but Neville believes Tottenham must act again immediately after four defeats out of four matches on his watch.
"If you're going to make another change, that for me needs to be today or tomorrow, because you don't wait," he said.
Tottenham are 16th in the Premier League, a point clear of Nottingham Forest and West Ham.
They face a daunting trip to Liverpool this weekend before a crunch match against Forest the following week.