The Urban Warriors have been on the hunt for a new shirt deal after MTN decided not to renew their sponsorship with the Cape Town club at the end of last season.
Efstathiou revealed that there have been positive signs in finding a new sponsor, yet nothing has yet been finalised.
“We’re still at it,” the Ajax boss told snl24.com/kickoff. “It’s looking better, but we haven’t confirmed anything yet. We have a couple of options.”
Efstathiou said it is highly doubtful that an agreement would be made before the end of the current transfer window, which would have provided a cash-injection to fund the arrival of new players.
“It’s very difficult,” he admitted. “You have to keep your business head intact, and go forward assuming you’re not going to get a sponsor.
“We’ve been extremely cautious, and the reality is that we’re unlikely to do it before the close of the transfer period.
“But I think we’ve managed to do pretty well with limited resources.”
Ajax have brought in the likes of James Mofokeng, Milton Ncube, Robin Ngalande, Phathizwe Sacolo and Clifford Mulenga, yet Efstathiou said he has had to be extremely cautious with transfer dealings in the market due to the club’s limited finances.
“You’ve got limitations,” he said. “You sometimes have to do transfer deals with players going out that you do not want to.
“But at the end of the day you run a business, and you’ve got to keep your books balanced. Your emotions say one thing, but your books do something else. But we’ve managed petty well, and we must just make sure we don’t put ourselves into trouble.”
Efstathiou says he would like to bring in another two players, but feels his sides’ unbeaten run after their first three league fixtures is testament to the current squad stepping up to the plate.
“Ideally we could do with two more players,” he said. “But sometimes in times like these, you get out of everybody else, and I think that’s what’s happened in the last three games.”
Ajax take on Bidvest Wits in their next League fixture at Athlone Stadium on Tuesday.