The Irons sacked Avram Grant after they were relegated from the Barclays Premier League.
Reports had suggested they would now move for Jones, with the Bluebirds having lost in the npower Championship play-offs.
In the frame: Dave Jones (centre right) is favourite for the West Ham job
However, Gold said on Twitter: 'Despite what you may have read in the papers, we have not spoken to Dave Jones.'
The 54-year-old former Wolves boss also appeared to rule himself out of the running. Quoted in the East London Advertiser, Jones said: 'I have not had any contact with them over the job.
Down and out: West Ham sacked Avram Grant after their relegation
'I am not prepared to say anything about the vacancy.
'I am still employed by Cardiff City and only thinking of them. I will be sitting down with the board at Cardiff and discussing my future with them soon.'
Former West Ham defender Chris Hughton, axed by Newcastle earlier in the season, is reported to be on the shortlist, as well as ex-Blackburn boss Sam Allardyce.
Whispers: David Gold (left) says he has not contacted Jones, despite reports
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Explore more:People: Sam Allardyce, Chris Hughton, David Gold Places: Newcastle, Cardiff