The Bluebirds finished in 18th place on 34 points and were sent back to the second tier after just a season in the Premier League.
Their campaign did end on a high, though, as they beat Manchester United 2-0 at Old Trafford on the final day.
Warnock still has one year left on his Cardiff contract and he looks set to target an immediate return to the Premier League.
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Chairman Mehmet Dalman confirmed he and chief executive Ken Choo held talks with the 70-year-old over a potential transfer budget and remain positive Warnock will remain in south Wales.
Dalman told the BBC: “He is the best man for the job, there was never any doubt in my mind.”
Warnock had wanted assurances over a budget that would allow him to bring in the players he felt were needed to mount a promotion challenge.