The initial deadline, set when they changed their name from Leeds in July, was for October 31.
But the club say that while they have made progress in their search, they require longer to conclude talks that could secure “significant” funding for their medium-term future.
A core group of individuals, who have previously supported the club, are said to have pledged financial backing on the basis of new ownership. That potential ownership will form a new company called Yorkshire Tykes Limited, which would own Carnegie.
A club statement read: “The directors believe that the level of funding under discussion would enable us to accelerate progress towards our vision and will also help to sustain that progress.
“Some of our new sources of funding could be made available now, but some will be deferred and some will be conditional.
“However, the significance of these opportunities has meant that the board of YTL has agreed with the current owners of Yorkshire Carnegie to extend the period of time over which it has an agreement to purchase the club until the end of the year.”
Carnegie chief executive Gary Hetherington added: “This potentially significant backing for the club, which would give it added support and security for the medium term, is a significant development that has come forward as a direct result of (chairman) Sir Ian McGeechan’s vision.
“We are planning further discussions, which we cannot complete in just a few days, over the next couple of months.”