Many are understandably reluctant to renew until the current managerial situation is resolved, but Steve warns that the risk of missing out on their regular seat is high for fans who miss the cut-off point.
He says: "I would advise supporters that they renew by Friday (June 8), because there is a good chance that they won't be able to purchase their own seat again after the deadline has passed.
"The club obviously understand that some fans are unsure about renewing their season tickets until a new manager is appointed. Because of that, supporters who are not happy with the choice of the new manager will be entitled to a full refund within seven days of the announcement being made."
Although season ticket renewal levels are at an average, a larger number of new applicants are expected, as Steve explains: "Renewals have been steady since the end of the season, on a par with last season.
"However, our reason for encouraging current holders to renew before the deadline has passed is that we are expecting a high number of new applicants due to our new discount offer for under-16s.
"The price of a child's season ticket has been reduced by around 75% - which the club believe are the cheapest Premier League under-16 prices in London.
"This has obviously created a lot of extra interest among families and younger supporters, and we are bracing ourselves for a rush of new applications next week.
"We hope supporters will understand that, by introducing this refund offer, we are committed to making sure their satisfaction is our priority."