With Ainslie out training with the team today and no sign of Kostecki, it appears Oracle have gone ahead and made changes to their afterguard.
Syndicate CEO Russell Coutts said skipper Jimmy Spithill will make the decision.
"You've got to remember, changing personnel at a time like this has never worked in the past so we've got to be cautious about making a change like that,'' Coutts told The Associated Press. "We wouldn't be thinking about it unless it had a really good chance at working.''
Coutts said Ainslie has the ability to make a difference.
"He's obviously an extremely accomplished sailor, but Jimmy and Ben and Tommy Slingsby haven't worked together yet,'' Coutts said. "That's a pretty big ask at this point in the regatta.''
Ainslie, who helms Oracle's 'B' boat, last night told Sky Sports UK he would be prepared to "step up" to the challenge if asked.
"For me personally it's about being part of the team, I'll do whatever the team wants me to do. If the decision is made that they want me to sail on the boat, of course I'd love to do that," the five-time Olympic medallist said.
"But at the same time I came into this team aware that my role was to support Jimmy Spithill and helm the second boat and I've been happy to fulfill that role, but if that changes then I'll step up to it."
Oracle have until 9am tomorrow local time to notify officials of any crew changes. Racing resumes tomorrow with a further two races scheduled.
Team NZ lead the first-to-nine series 4-0, with Oracle still to clear one penalty point before they can start scoring.
This morning's front page of the New Zealand Herald: