The Bluebirds will renew their quest for an automatic promotion spot when they face Middlesbrough on Monday.
Jones has previously managed in the top flight with Southampton and Wolves but parted company with the latter amid wranglings over an apparent lack of financial support from the club's board.
"Yes I have unfinished business," Jones told the Western Mail. "But you have unfinished business in whatever you do because you should never be happy with what you've got.
"I am very proud of what I've done here but I would be even prouder of taking the club into the Premier League.
"I am honoured to be manager of Cardiff City and proud of what we're trying to do. But I hope when I leave, like all the other clubs I've been at, I leave a legacy that people can build from - that's my job and I will never stop."