Spurs do not have a venue lined up if they are drawn at home in the third round of the competition scheduled for September 25-26.
Wembley is unavailable that week and their new 62,000-seat stadium will not be ready until the end of October at the earliest.
Now the club have spoken to the Tottenham Hotspur Supporters’ Trust who have launched an online survey asking fans if they would prefer a neutral ground or to reverse the tie. They can also opt for ‘no preference’.
Tottenham are one of seven clubs involved in European competition entering the Carabao Cup at the third-round stage and with the draw unseeded they could potentially play Arsenal, Chelsea, Liverpool or one of the two Manchester clubs.
Reversing the fixture would not be ideal as Tottenham are looking to win their first trophy under Mauricio Pochettino. They would also have to compensate their opponents.
It remains unclear whether the new stadium will be ready in time for the home Premier League game against Manchester City on October 28.
With Wembley staging an NFL game that day it is possible the fixture will be put back a day.
Spurs beat Fulham 3-1 at the national stadium last Saturday and have confirmed they will host league games at Wembley against Liverpool and Cardiff.
That will take place on either the week commencing September 17 or October 1.