Franz Tost hopes Toro Rosso will have a new engine deal in place "before the end of the season" as negotiations continue.
The midfield team is without an engine supplier for 2016 after Red Bull decided to part ways with the under-performing Renault.
Toro Rosso, though, are closing in on a new deal that is believed to be with Ferrari.
"We are still negotiating, and we are getting closer and closer, and within the next weeks we will have a decision," team principal Tost told Autosport.
"I hope it will be before the end of the season because otherwise it will become very tough for the start in Melbourne, especially as the calendar has changed and it [the start] is two weeks earlier than before."
As for reports that it could be a year-old Ferrari unit that powers the STR11, Tost concedes Toro Rosso will need to take what they can get.
He said: "The manufacturers decide what we get, and in the end we have to be happy to get something.
"If it's one year old, this is how it is. The influence we have in this case is not on a level we maybe would expect, or wish.
"Therefore with this regulation and this situation we have to take what they offer us."