A local newspaper claimed Jones' future was on the agenda of an emergency board meeting after back-to-back festive thrashings by Bristol City and Watford.
But Jones described the "phantom board meeting" as "total rubbish" and insists he wants to lead Cardiff to promotion.
"It's easy for people to say it is time to change," said Bluebirds boss Jones.
The Welsh club, last season's beaten Championship play-off finalists, enjoyed time at the summit of the Championship at the end of October following successive hammerings of Leeds United and Norwich.
But Cardiff have stuttered since and picked up just eight points from a possible 30 while Leeds, who visit the Cardiff City Stadium on Tuesday, are unbeaten after their 4-0 Elland Road lesson by Cardiff back on 25 October.
The Wales On Sunday reported that Cardiff chiefs had called a board meeting for Sunday following Saturday's 3-0 defeat at Bristol City where Jones' position was "under the spotlight."
But Jones dismissed there was such a summit, claiming the reports were "total rubbish" and that the meeting was to finalise the signing of John Parkin from Preston North End.
Cardiff boast a star-studded squad at Championship level that includes recent England call-up Jay Bothroyd, on-loan Manchester City striker Craig Bellamy, £4m man Michael Chopra and last season's Championship top-scorer Peter Whittingham.
The Bluebirds were installed as favourites for promotion to the Premier League after their summer signing spree when Jason Koumas, Seyi Olofinjana, Andy Keogh and Danny Drinkwater joined Bellamy at the Cardiff City Stadium.
Jones admits this is the best squad he has assembled since taking the Cardiff hot-seat in the summer of 2005 - and he has already added striker Parkin in the first of an expected signing spree in the January transfer window.
The Cardiff boss has resided over a club, previously beset with financial uncertainty, that had been forced to sell a player a season to survive.
And the Bluebirds survived a host of High Court visits in 2010 facing winding-up orders for unpaid tax as a protracted take-over by a Malaysian-led consortium was finalised.
But since paying their debts, including a £1.3m bill to HM Revenue and Customs, and the lifting of a close-season transfer embargo, Cardiff are now looking to end their 49-year top-flight exile in English football backed by millionaire property developer Tan Sri Vincent Tan Chee Yioun.
So Cardiff's poor run - just Coventry City and Scunthorpe United are below them in the form table - has heaped pressure on Jones.
But the Cardiff manager hit back, saying: "Sadly certain people love a negative drama, I'll just keep going and keep doing the job I get paid for and love.
"Even though I'm getting all the flack which I can never stop, I'll have to fight it and get on with it. I have quite broad shoulders and they have to be with the job I am in.
"I'm a big boy and have been through worst things in my life to worry about speculation and rumours.
"This is my livelihood. I've fought hard to get this club where it is, I've fought hard to get where my life is.
"The easy option is to say 'get rid.' As a manager when players aren't performing the easy option is to get rid and get someone else in. That is not the way it works.
"The frustrating thing is we're not getting the results that we want. But I believe in what my players are trying to do and I believe they can turn it around.
"We have to stay strong and be big and say I'm big enough to take all this. I'm looking for my big characters.
"There is always pressure on. The pressure that is put on us is enormous because we put it on ourselves because we want to win and do well.
"When the times aren't always good we still stick together and work harder, not just throw it away otherwise you'll be going through players and managers every time you lost a football match.
"And with all the things that are said, we're still up there in the table. We're still in a fantastic position with what we've done in last couple of months."
Fourth-placed Leeds or fifth-placed Cardiff could move into the Championship's top two with victory at the Cardiff City Stadium on Tuesday.
Source: BBC Sport